Abstract

Particle identity and entanglement are two fundamental quantum properties that work as major resources for various quantum information tasks. However, it is still a challenging problem to understand the correlation of the two properties in the same system. While recent theoretical studies have shown that the spatial overlap between identical particles is necessary for nontrivial entanglement, the exact role of particle indistinguishability in the entanglement of identical particles has never been analyzed quantitatively before. Here, we theoretically and experimentally investigate the behavior of entanglement between two bosons as spatial overlap and indistinguishability simultaneously vary. The theoretical computation of entanglement for generic two bosons with pseudospins is verified experimentally in a photonic system. Our results show that the amount of entanglement is a monotonically increasing function of both quantities. We expect that our work provides an insight into deciphering the role of the entanglement in quantum networks that consist of identical particles.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Entanglement is one of the most significant quantum features, playing a principal role in the study of both quantum foundation and quantum information. A given entangled system cannot be characterized as a simple collection of individual subsystems, even when they are space-like separated [1,2]. It is also a crucial resource of various quantum tasks including quantum computation [3], quantum communication [4,5], and quantum sensing [6].

However, while the entanglement between non-identical particles is mathematically well-described as the superposition of different multipartite states [7], its formalism cannot be directly applied to the case of identical particles. A set of identical particles has the exchange symmetry [8], which makes the Hilbert space of the particles non-factorizable, and thus, every state of identical particles becomes a superposed multipartite state in the first quantization language. Hence, one can say that any particles that are identical to each other are entangled even when they are prepared in worlds apart [9], which seems implausible. This is called the non-factorization problem of identical particles [1012].

To solve this puzzle, we need to discard unphysical entanglement from the physical one. Such unphysical entanglement is merely mathematical and, therefore, it cannot be extracted by any physical setup [1322]. Indeed, when we say a multipartite system has nontrivial entanglement, the entanglement can be detected by registers that are distinguishable to each other [23,24]. There are several approaches to formally define the entanglement of identical particles to overcome the non-factorization problem of identical particles. The recent crucial formalisms include algebraic approaches [10,25], the second quantization approach [2628], no-labeling approach [2931], and the first quantization approach (1QL) [32]. All these formalisms provide criteria to distinguish the mathematical entanglement from physically extractable entanglement by using exchange symmetry. The mathematical connection among the aforementioned approaches is explained in Ref. [33] from the viewpoint of the partial trace.

One of the imperative queries closely related to the above studies on the entanglement of identical particles is: under what conditions can a set of identical particles carry physical entanglement? Answering this question not only provides an insight to understand the fundamental property of entanglement, but also practically helps to construct quantum systems that employ identical particles as information processing resource [34]. It is well-known that such set is able to possess entanglement only when the particles spatially overlap [31,35,36], or more rigorously speaking when non-zero spatial coherence between particles and detectors exists [32]. Hence, one can surmise that the particle indistinguishability and spatial overlap are two key factors for identical particles to be entangled. On the other hand, while theoretical studies on the quantitative relation of entanglement to spatial overlap alone have been executed before [31,32,36], which are experimentally verified in some recent works [37,38] there has been no attempt to examine the effect of both indistinguishability and spatial overlap to the entanglement of identical particles at the same time either theoretically or experimentally.

In this paper, we theoretically predict the quantitative relation of entanglement between two bosons with particle indistinguishability and spatial overlap using recently proposed partial trace technique [2931], which is then experimentally verified using photons. We show that the amount of entanglement, which is quantified as concurrence, is a monotonically increasing function of both indistinguishability and spatial overlap. The obtained data confirm that two kinds of quantum properties, i.e., particle indistinguishability and spatial overlap, cooperate to generate entanglement.

2. Theory

This section presents a theoretical analysis on entanglement generation among identical particle with respect to the particle indistinguishability and spatial overlap. Since the conceptual distinction between particle identity and distinguishability can be subtle, we briefly explain it in Supplement 1.

We first introduce a formalism for calculating the entanglement between two bosons in the generic system. Then, we derive a formula for the concurrence to investigate the behavior of entanglement with the variation of the distinguishability and spatial overlap.

Suppose that we have a system of two bosons that are in the states ($\Psi _A$, $\Psi _B$). Then, from the exchange symmetry of bosons, the total state $|\Psi \rangle$ can be written as

$$|\Psi\rangle = |\Psi_A,\Psi_B\rangle,$$
with the symmetry relation
$$|\Psi_A,\Psi_B\rangle = |\Psi_B,\Psi_A\rangle.$$
The transition relations between two different wave functions are given by [29]
$$\begin{aligned} \langle \Psi_C, \Psi_D|\Psi_A,\Psi_B\rangle &= \langle\Psi_C|\Psi_A\rangle\langle\Psi_D|\Psi_B\rangle + \langle\Psi_C|\Psi_B\rangle\langle\Psi_D|\Psi_A\rangle,\\ \langle\Psi_C|\Psi_A,\Psi_B\rangle &= \frac{1}{\sqrt{2}}\Big[\langle\Psi_C|\Psi_A\rangle|\Psi_B\rangle +\langle\Psi_C|\Psi_B\rangle|\Psi_A\rangle\Big]. \end{aligned}$$
The above relations can be derived explicitly using the first quantization language (see Supplement 1).

Since our goal is to clarify the role of indistinguishability and spatial overlap in the generation of entanglement, we need three degrees of freedom to present the particle states, i.e., internal pseudospin (which will be detected at the output modes, defining in which degree of freedom the entanglement will be found), distinguishability function, and spatial distribution function. Hence, $\Psi _i$ ($i=A,B$) are now specified as $\Psi _i = (\psi _i, s_i, \phi _i)$ where $\psi _i$ is the spatial wave function, $s_i$ is the spin value, and $\phi _i$ is the particle distinguishability. In our experimental setup in Section 3., $(s_i,\phi _i)$ are realized as polarizations and temporal modes. However, it is not inherent at all to impose the role of physical quantities in such a way. The role of polartizations and temporal modes can be reversed, or any internal properties for a given physical setup can play the role of ($s_i, \phi _i$).

Considering that the result becomes trivial for $s_A=s_B$, we restrict our case into $(s_A,s_B) = (\uparrow ,\downarrow )$. The total state of two bosons is now presented as

$$|\Psi\rangle = |(\psi_A, \uparrow, \phi_A), (\psi_B,\downarrow,\phi_B)\rangle.$$
Note that at this point one cannot tell about the entanglement of $|\Psi \rangle$, since Eq. (4) says nothing about the spatial relation of particles to detectors. On the other hand, the entanglement of identical particles depends not only on the particles’ initial state but also the detector setup, i.e., how detectors are spatially distributed related to the particle and which quantity the detectors can measure [32,36].

In order for a multipartite system to have physical entanglement, the subsystems should be individually accessible by observers [39]. In addition, we consider the entanglement of general bosons, which conserve particle number superselection rule (SSR) [40], by which massive bosonic states with different particle number distributions cannot be coherent. One of such entanglement measures is the entanglement of particles introduced in Ref. [23], which is defined as

$$E_{P}(|\Psi\rangle) = \sum_{\vec{N}}p_{\vec{N}}E(|\Psi\rangle_{\vec{N}}),$$
where $\vec {N} = (n_L,n_R)$ is a possible number distribution vector ($n_R$ and $n_L$ is the number of particles in the right and left detector with $n_R + n_L=N$), $p_{\vec {N}}$ is the probability for a given state $|\Psi \rangle$ to have a number distribution $\vec {N}$, and $|\Psi \rangle _{\vec {N}}$ is the partial state of $|\Psi \rangle$ that has $\vec {N}$. $E_P$ is one of practical entanglement measures for identical particles, for it is handily transferred to digital quantum registers with local operations [41]. Since we deal with two particles, our setup needs two detectors $L$ and $R$ that are located in distinctive places (spatially separated, i.e., $\langle{L |R}\rangle=0$) that can measure the superposition of wavefunctions with the same particle number distribution but different internal states.

Figure 1 is a conceptual diagram to extract physical entanglement from two bosons. Since we are interested in the case only when two particles are detected at two observers $L$ and $R$, the spatial relations of the particles to the detectors are expressed in the most general form as

$$|\psi_A\rangle = \alpha_l|L\rangle + \alpha_r|R\rangle, \quad |\psi_B\rangle = \beta_l|L\rangle + \beta_r|R\rangle,$$
where $\{\alpha _r,\alpha _l,\beta _r,\beta _l\}$ are complex numbers and satisfy $|\alpha _l|^{2} + |\alpha _r|^{2} =|\beta _l|^{2} + |\beta _r|^{2} =1$. Then, Eq. (4) can be rewritten in terms of the detector basis $\{|L\rangle,|R\rangle\}$ as
$$\begin{aligned} |\Psi\rangle =&\alpha_l\beta_l |(L,\uparrow,\phi_A),(L,\downarrow,\phi_B)\rangle + \alpha_l\beta_r|(L,\uparrow,\phi_A),(R,\downarrow,\phi_B)\rangle\\ &+\alpha_r\beta_l|(L,\downarrow,\phi_B),(R,\uparrow,\phi_A)\rangle + \alpha_r\beta_r |(R,\uparrow,\phi_A),(R,\downarrow,\phi_B)\rangle. \end{aligned}$$
Of the four terms in the right hand side of Eq. (7), we see that $|\Psi \rangle _{(2,0)}$ is the first one, $|\Psi \rangle _{(0,2)}$ is the fourth one, and $|\Psi \rangle _{(1,1)}$ is a superposition of the second and third one. Here, $|\Psi \rangle _{(n_R,n_L)}$ denotes a partial state of $|\Psi \rangle$ with the particle number distribution $(n_R,n_L)$. Hence, according Eq. (5), only the second and third terms can contribute to $E_P$. This is detected in the experimental setup by postselecting states without particle bunching.

 figure: Fig. 1.

Fig. 1. Generic setup for detecting entanglement of two identical particles: The spatially overlapped particles have internal spins ($\uparrow$ and $\downarrow$) and distinguishability (represented as two different colors, red and blue, in the figure). Two detectors located at $L$ and $R$ indicate the spins of the particles.

Download Full Size | PPT Slide | PDF

Since we are supposed to measure only the pseudospin states, the actually measured particle state is that which the distinguishability part of $|\Psi \rangle _{\vec {N} =(1,1)}$ is traced out. By defining the complete orthonormal basis of particle distinguishability as $\{|X_a\rangle\}$ so that

$$\sum_{a}\langle\phi|X_a\rangle\langle{X_a|\phi}\rangle=1$$
holds for any $\phi$, the measured density matrix $\rho _{(1,1)}^{m}$ is given by
$$\rho^{m}_{(1,1)} = \sum_{a,b} \langle(L,X_a),(R,X_b)|\Psi\rangle\langle\Psi|(L,X_a),(R,X_b)\rangle.$$
The transition relations in Supplement 1 give
$$\langle(L,X_a),(R,X_b)|(L,\uparrow,\phi_1),(R,\downarrow,\phi_2) \rangle =\langle{X_a|\phi_1}\rangle\langle{X_b|\phi_2}\rangle |(L,\uparrow),(R,\downarrow)\rangle,$$
and so on, by which we obtain
$$\begin{aligned} \rho^{m}_{(1,1)} =& |\alpha_l\beta_r|^{2} |(L,\uparrow),(R,\downarrow)\rangle\langle(L,\uparrow),(R,\downarrow)| + |\alpha_r\beta_l|^{2} |(L,\downarrow),(R,\uparrow)\rangle\langle(L,\downarrow),(R,\uparrow)|\\ &+ \alpha_l\beta_r\alpha_r^{*}\beta_l^{*}|\langle\phi_1|\phi_2\rangle|^{2} |(L,\uparrow),(R,\downarrow)\rangle\langle(L,\downarrow),(R,\uparrow)|\\ &+\alpha_l^{*}\beta_r^{*}\alpha_r\beta_l|\langle\phi_1|\phi_2\rangle|^{2}|(L,\downarrow),(R,\uparrow)\rangle\langle(L,\uparrow),(R,\downarrow)|. \end{aligned}$$
The last two terms of the above equation contribute to the non-trivial entanglement. Note that the success probability $p_s$ of the transformation from Eq. (7) to Eq. (11) can be less than 1, depending on the spatial mode distribution and detector setups.

The concurrence of the state $\rho ^{m}_{(1,1)}$, which quantifies the amount of $E_P$, is computed using the definition in Ref. [42,43] as

$$C= 4|\alpha_l\alpha_r\beta_l\beta_l|\cdot|\langle\phi_A|\phi_B\rangle|^{2}.$$
Here, $4|\alpha _l\alpha _r\beta _l\beta _l|$ and $|\langle\phi _A|\phi _B\rangle|^{2}$ represent the spatial overlap and the particle indistinguishability respectively.

Equation 12 shows that the concurrence is determined by three variables, $|\alpha _l|$, $|\beta _l|$, and $|\langle\phi _A|\phi _B\rangle|$. The particles are unentangled when they are completely distinguishable, i.e., $\langle\phi _1|\phi _2\rangle=0$, or when one of the particles is detected at only one side, i.e., one of $\{\alpha _l,\alpha _r,\beta _l, \beta _r\}$ is zero. On the other hand, the particles are maximally entangled when the indistinguishability and spatial overlap are both maximal, i.e., $|\langle\phi _1|\phi _2\rangle|=1$ and $|\alpha _l| = |\beta _l|=\frac {1}{\sqrt {2}}$.

3. Experiment

In an optical system, photons are the identical particles and the photon polarization $\{|H\rangle ,|V\rangle \}$ compose the spin $\{|\downarrow \rangle ,|\uparrow \rangle \}$, where $|H\rangle$ and $|V\rangle$ denote the horizontal and vertical polarization states, respectively. Particle distinguishability can be controlled by other degrees of freedom such as momenta, spectra, and temporal modes. Here, it is controlled by the temporal modes of single photons.

The identical photon pairs, centered at 780 nm, were generated at a type-II BBO crystal via spontaneous parametric down conversion pumped by a femtosecond pulse at 390 nm [44,45]. To guarantee the spectral and spatial indistinguishability, two photons were filtered by 3 nm bandpass interference filters (IF) at 780 nm, then collected by single-mode fibers (SMF). Next, they were sent to the experimental setup shown in Fig. 2 in order to investigate entanglement behavior via particle indistinguishability and spatial overlap.

 figure: Fig. 2.

Fig. 2. The experimental setup to entangling photons via their spatial overlap and indistinguishability. Pol. : polarizer, H$^{*}$ : half waveplate at $\theta$, BD : beam displacer, H$_{45}$ : half waveplate at 45$^{\circ }$, WP : waveplates, PBS : polarizing beamsplitter, D1-D4 : single photon detectors, CCU : coincidence counting unit. The optical delay $l$ of a photon has been scanned in order to introduce the particle indistinguishability.

Download Full Size | PPT Slide | PDF

The initial polarization states of the incoming photons $A$ and $B$ were configured by polarizers (Pol.) and half waveplates (HWP, H$^{*}$). Then, its probability amplitudes were divided into two spatial modes by a beam displacer (BD1) which transmits and reflects horizontal and vertical polarization states, respectively. The HWP at $45^{\circ }$ ($\textrm {H}_{45}$) at spatial modes $\alpha _L$ and $\beta _L$ converted the polarization states from horizontal to vertical and vice versa. Therefore, the polarization states of photon $A$ and $B$ became vertical and horizontal, respectively, regardless of the spatial modes. Subsequently, the spatial modes $\alpha _R$ and $\beta _R$ ($\alpha _L$ and $\beta _L$) were combined by BD2 (BD3) which corresponds to the spatial wavefunction overlap. The two-qubit polarization state $\rho _{\textrm {ex}}$ at the outputs of BD2 and BD3 ($L$ and $R$) was reconstructed via two-qubit quantum state tomography (QST) with maximum likelihood estimation. The waveplates (WP) and polarizing beamsplitters (PBS) were utilized to perform various projective measurements for QST [46,47]. The coincidence counts were registered by a home-made coincidence counting unit (CCU) [48].

 figure: Fig. 3.

Fig. 3. Coincidence counts with respect to scanning the optical delay. A HOM dip can be observed for the coincidences D12 (experimental data and fitting curve in red) and D34 (experimental data and fitting curve in blue), the visibilities were $V=0.99\pm 0.04$ and $V=0.91\pm 0.05$, respectively. The error bars represent one standard deviation due to Poissonian counting statistics.

Download Full Size | PPT Slide | PDF

The experimental setup faithfully demonstrates the conceptual diagram of Fig. 1. The degree of spatial overlap at $L$ and $R$ could be adjusted by changing the initial polarization states. By using $|H\rangle$ transmitting polarizers and HWPs at $\theta$, the initial polarization state becomes $\cos 2\theta |H\rangle +\sin 2\theta |V\rangle$. Note that we set the same initial polarization states for the photons $A$ and $B$ in order to investigate the symmetrical spatial overlap case. After BD1, the coefficients of polarization state are transferred to the probability amplitudes of spatial modes, so $\alpha _L=\beta _R=\sin 2\theta$ and $\alpha _R=\beta _L=\cos 2\theta$. Therefore, one can find the degree of spatial overlap becomes

$$4|\alpha_L\alpha_R\beta_L\beta_R|=\sin^{2}{4\theta}.$$

The degree of distinguishability can be tuned by changing one of the photons arrival time at the BDs. This can be done by scanning one of the input photons, see the optical delay $l$ of Fig. 2. Lastly, the successful case in which only one particle is found at $L$ and the other at $R$ can be post-selected by coincidences between $L$ and $R$. Note that one can trace out the indistinguishability wavefunction $\phi _i$ if the coincidence window is larger than the timing difference between $A$ and $B$, so the timing information is not registered. Assuming that the degree of distinguishability is presented as a Gaussian function with the center $l=0$, Eq. (12) can be rewritten with the variables of our optical system as

$$C= \sin^{2}{4\theta}\exp\left[-\frac{ l^{2}}{2\sigma^{2}} \right].$$
The derivation of Eq. (14) is explained in detail in Supplement 1.

 figure: Fig. 4.

Fig. 4. Concurrence with respect to (a) particle distinguishability, and (b) spatial overlap, respectively. The particle distinguishability is adjusted by the optical delay $l$, and the spatial overlap is controlled by the angle $\theta$ of the H$_{\theta }$. The error bars present the one standard deviation from 100 reconstructed two-qubit states $\rho _{\textrm {ex}}$ by taking into account the Poisson statistics in measured coincidence counts.

Download Full Size | PPT Slide | PDF

The distinguishability introduced by the optical delay $l$ can be measured by the Hong-Ou-Mandel (HOM) interference at BD2 and BD3. Figure 3 presents two-fold coincidences of D12 and D34 with respect to the optical delay $l$ where Dij stands for the coincidences between Di and Dj. The input polarization state was prepared as $|++\rangle$ where $|+\rangle =\frac {1}{\sqrt {2}}(|H\rangle +|V\rangle )$ in order to measure the HOM interference at BD2 and BD3, simultaneously. The HOM dip at $l=0$ implies that the two photons $A$ and $B$ are indistinguishable. The HOM interferences of D12 and D34, which can be fitted with the Gaussian function with the full width at half maximum (FWHM), are $132\pm 4\;\mu \textrm {m}$ and $137\pm 4\;\mu \textrm {m}$, respectively. These widths coincide with the coherence length of the photon pair which is determined by the bandwidth of IF. The HOM visibility, defined by the relative depth of the dip to the non-interfering counts, was measured as $V=0.99\pm 0.04$ and $V=0.91\pm 0.05$ for D12 and D34, respectively. To investigate the role of particle indistinguishability for generation of entanglement, we have analyzed two-qubit polarization states at various optical delays of $L_0=0\;\mu \textrm {m}$, $L_1=30\;\mu \textrm {m}$, $L_2=60\;\mu \textrm {m}$, and $L_3=300\;\mu \textrm {m}$.

Figure 4(a) presents concurrence as a function of optical delay $l$ at different HWP $\textrm {H}^{*}$ angles $\theta$. The concurrence is calculated from the experimentally reconstructed two-qubit state $\rho _{\textrm {ex}}$ [42,43,49]. It corresponds to the amount of entanglement with respective to particle distinguishability with fixed different degrees of spatial overlap. It clearly shows that concurrence decreases as the optical delay increases, or equivalently the distinguishability of particles increase. The experimental data are fitted with a Gaussian function with the FWHM of $140\;\mu \textrm {m}$, comparable to that of HOM interference.

Figure 4(b) represents concurrence as a function of the HWP $\textrm {H}^{*}$ angle $\theta$ at different optical delays $l$. Note that $\theta =0^{\circ }$ and $22.5^{\circ }$ correspond to non-spatial overlap and complete spatial overlap cases, respectively. It clearly presents that the amount of entanglement increase as the spatial overlap increases. As expected from Eq. (13), the experimental data are fitted with $C=C_0\sin ^{2}{4\theta }$, where $C_0$ corresponds to the maximum concurrence at a given optical delay $l$, and $\theta$ in radian.

4. Discussion

In this work, we have investigated the quantitative relation of the entanglement between identical particles with particle indistinguishability and spatial overlap from the perspectives of theory and experiment. The entanglement concurrence of two oppositely polarized photons decreases with decreasing particle indistinguishability and spatial overlap, which fits in well with the theoretical predictions for the entanglement of identical particles in the generic boson system. While the theory has been developed in the most general format, our linear optical experiment setup can be analyzed with other techniques e.g., Feynman path formalism or quantum walk [44].

In addition, our analysis can be applied to various quantum information processing utilizing identical particles as media of information. For example, the computational difficulty of the boson sampling problem [50] is known to have a close relation with the distinguishability [51,52] and the spatial distribution of photons [53]. We expect that our work provides an insight into understanding the role of the entanglement of identical particles in quantum information processing such as linear optical quantum computing. In addition, our method can also be applied to fermions. They follow the parity SSR [40,54], which makes the entanglement of fermions more complicated as well as intriguing [55,56].

Funding

Korea Institute of Science and Technology (2E30620); Institute for Information and Communications Technology Promotion (2020-0-00947, 2020-0-00972); National Research Foundation of Korea (2015R1A6A3A04059773, 2019M3E4A1079526, 2019M3E4A1079666, 2019R1A2C2006381, 2019R1I1A1A01059964).

Disclosures

The authors declare no conflicts of interest.

See Supplement 1 for supporting content.

References

1. A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47(10), 777–780 (1935). [CrossRef]  

2. J. S. Bell, Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy (Cambridge university, 2004).

3. T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010). [CrossRef]  

4. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991). [CrossRef]  

5. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993). [CrossRef]  

6. L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002). [CrossRef]  

7. E. Schrödinger, in Mathematical Proceedings of the Cam- bridge Philosophical Society, 31555–563 (1935).

8. P. A. M. Dirac, The principles of quantum mechanics (Oxford university, 1981).

9. A. Peres, Quantum theory: concepts and methods, Vol. 57 (Springer, 2006).

10. A. Balachandran, T. Govindarajan, A. R. de Queiroz, and A. Reyes-Lega, “Algebraic approach to entanglement and entropy,” Phys. Rev. A 88(2), 022301 (2013). [CrossRef]  

11. V. Balasubramanian, B. Craps, T. De Jonckheere, and G. Sàrosi, “Entanglement versus entwinement in symmetric product orbifolds,” J. High Energy Phys. (online) 2019(1), 190 (2019). [CrossRef]  

12. S. Chin and J.-H. Chun, “Taming identical particles for discerning the genuine nonlocality,” arXiv:2002.03784 (2020).

13. J. Schliemann, D. Loss, and A. H. MacDonald, “Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots,” Phys. Rev. B 63(8), 085311 (2001). [CrossRef]  

14. J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001). [CrossRef]  

15. G. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,” Nuovo Cim. B 39(1), 130–134 (1977). [CrossRef]  

16. G. Ghirardi, L. Marinatto, and T. Weber, “Entanglement and Properties of Composite Quantum Systems: a Conceptual and Mathematical Analysis,” J. Stat. Phys. 108(1/2), 49–122 (2002). [CrossRef]  

17. K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, “Quantum Correlations in Systems of Indistinguishable Particles,” Ann. Phys. 299(1), 88–127 (2002). [CrossRef]  

18. R. Paskauskas and L. You, “Quantum correlations in two-boson wave functions,” Phys. Rev. A 64(4), 042310 (2001). [CrossRef]  

19. P. Zanardi, “Quantum entanglement in fermionic lattices,” Phys. Rev. A 65(4), 042101 (2002). [CrossRef]  

20. Y. Shi, “Quantum entanglement of identical particles,” Phys. Rev. A 67(2), 024301 (2003). [CrossRef]  

21. H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004). [CrossRef]  

22. H. Barnum, G. Ortiz, R. Somma, and L. Viola, “A generalization of entanglement to convex operational theories: entanglement relative to a subspace of observables,” Int. J. Theor. Phys. 44(12), 2127–2145 (2005). [CrossRef]  

23. H. Wiseman and J. A. Vaccaro, “Entanglement of Indistinguishable Particles Shared between Two Parties,” Phys. Rev. Lett. 91(9), 097902 (2003). [CrossRef]  

24. N. Killoran, M. Cramer, and M. B. Plenio, “Extracting Entanglement from Identical Particles,” Phys. Rev. Lett. 112(15), 150501 (2014). [CrossRef]  

25. A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett. 110(8), 080503 (2013). [CrossRef]  

26. F. Benatti, R. Floreanini, and U. Marzolino, “Entanglement and squeezing with identical particles: ultracold atom quantum metrology,” J. Phys. B 44(9), 091001 (2011). [CrossRef]  

27. F. Benatti, R. Floreanini, and U. Marzolino, “Bipartite entanglement in systems of identical particles: the partial transposition criterion,” Ann. Phys. 327(5), 1304–1319 (2012). [CrossRef]  

28. A. C. Lourenco, T. Debarba, and E. I. Duzzioni, “Entanglement of indistinguishable particles: A comparative study,” Phys. Rev. A 99(1), 012341 (2019). [CrossRef]  

29. R. L. Franco and G. Compagno, “Quantum Entanglement of Identical Particles by Standard Information-Theoretic Notions,” Sci. Rep. 6(1), 20603 (2016). [CrossRef]  

30. R. L. Franco and G. Compagno, “Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing,” Phys. Rev. Lett. 120(24), 240403 (2018). [CrossRef]  

31. G. Compagno, A. Castellini, and R. L. Franco, “Dealing with indistinguishable particles and their entanglement,” Phil. Trans. R. Soc. A 376(2123), 20170317 (2018). [CrossRef]  

32. S. Chin and J. Huh, “Entanglement of identical particles and coherence in the first quantization language,” Phys. Rev. A 99(5), 052345 (2019). [CrossRef]  

33. S. Chin and J. Huh, “Reduced density matrix of nonlocal identical particles,” arXiv:1906.00542 (2019).

34. C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002). [CrossRef]  

35. N. Paunkovic, The role of indistinguishability of identical particles in quantum information processing, Ph.D. thesis, Oxford university (2004).

36. M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013). [CrossRef]  

37. F. Nosrati, A. Castellini, G. Compagno, and R. L. Franco, “Robust entanglement preparation against noise by controlling spatial indistinguishability,” npj Quant. Inf. 6(1), 39 (2020). [CrossRef]  

38. K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

39. B. Dalton, J. Goold, B. Garraway, and M. Reid, “Quantum entanglement for systems of identical bosons: I. General features,” Phys. Scr. 92(2), 023004 (2017). [CrossRef]  

40. G. C. Wick, A. S. Wightman, and E. P. Wigner, “The Intrinsic Parity of Elementary Particles,” Phys. Rev. 88(1), 101–105 (1952). [CrossRef]  

41. A. Vaccaro, F. Anselmi, and H. Wiseman, “Entanglement of identical particles and reference phase uncertainty,” Int. J. Quant. Inform. 01(04), 427–441 (2003). [CrossRef]  

42. S. Hill and W. K. Wootters, “Entanglement of a Pair of Quantum Bits,” Phys. Rev. Lett. 78(26), 5022–5025 (1997). [CrossRef]  

43. W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80(10), 2245–2248 (1998). [CrossRef]  

44. Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018). [CrossRef]  

45. T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019). [CrossRef]  

46. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001). [CrossRef]  

47. T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019). [CrossRef]  

48. B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54(15), 4727–4731 (2015). [CrossRef]  

49. Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8(2), 117–120 (2012). [CrossRef]  

50. S. Aaronson and A. Arkhipov, inProceedings of the forty- third annual ACM symposium on Theory of computing (ACM, 2011) pp. 333–342.

51. V. Shchesnovich, “Partial indistinguishability theory for multiphoton experiments in multiport devices,” Phys. Rev. A 91(1), 013844 (2015). [CrossRef]  

52. M. C. Tichy, “Sampling of partially distinguishable bosons and the relation to the multidimensional permanent,” Phys. Rev. A 91(2), 022316 (2015). [CrossRef]  

53. S. Chin and J. Huh, “Majorization and the time complexity of linear optical networks,” J. Phys. A: Math. Theor. 52(24), 245301 (2019). [CrossRef]  

54. G.-C. Wick, A. S. Wightman, and E. P. Wigner, “Superselection Rule for Charge,” Phys. Rev. D 1(12), 3267–3269 (1970). [CrossRef]  

55. N. Friis, “Reasonable fermionic quantum information theories require relativity,” New J. Phys. 18(3), 033014 (2016). [CrossRef]  

56. N. Gigena and R. Rossignoli, “Bipartite entanglement in fermion systems,” Phys. Rev. A 95(6), 062320 (2017). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47(10), 777–780 (1935).
    [Crossref]
  2. J. S. Bell, Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy (Cambridge university, 2004).
  3. T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
    [Crossref]
  4. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
    [Crossref]
  5. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
    [Crossref]
  6. L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
    [Crossref]
  7. E. Schrödinger, in Mathematical Proceedings of the Cam- bridge Philosophical Society, 31555–563 (1935).
  8. P. A. M. Dirac, The principles of quantum mechanics (Oxford university, 1981).
  9. A. Peres, Quantum theory: concepts and methods, Vol. 57 (Springer, 2006).
  10. A. Balachandran, T. Govindarajan, A. R. de Queiroz, and A. Reyes-Lega, “Algebraic approach to entanglement and entropy,” Phys. Rev. A 88(2), 022301 (2013).
    [Crossref]
  11. V. Balasubramanian, B. Craps, T. De Jonckheere, and G. Sàrosi, “Entanglement versus entwinement in symmetric product orbifolds,” J. High Energy Phys. (online) 2019(1), 190 (2019).
    [Crossref]
  12. S. Chin and J.-H. Chun, “Taming identical particles for discerning the genuine nonlocality,” arXiv:2002.03784 (2020).
  13. J. Schliemann, D. Loss, and A. H. MacDonald, “Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots,” Phys. Rev. B 63(8), 085311 (2001).
    [Crossref]
  14. J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001).
    [Crossref]
  15. G. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,” Nuovo Cim. B 39(1), 130–134 (1977).
    [Crossref]
  16. G. Ghirardi, L. Marinatto, and T. Weber, “Entanglement and Properties of Composite Quantum Systems: a Conceptual and Mathematical Analysis,” J. Stat. Phys. 108(1/2), 49–122 (2002).
    [Crossref]
  17. K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, “Quantum Correlations in Systems of Indistinguishable Particles,” Ann. Phys. 299(1), 88–127 (2002).
    [Crossref]
  18. R. Paskauskas and L. You, “Quantum correlations in two-boson wave functions,” Phys. Rev. A 64(4), 042310 (2001).
    [Crossref]
  19. P. Zanardi, “Quantum entanglement in fermionic lattices,” Phys. Rev. A 65(4), 042101 (2002).
    [Crossref]
  20. Y. Shi, “Quantum entanglement of identical particles,” Phys. Rev. A 67(2), 024301 (2003).
    [Crossref]
  21. H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004).
    [Crossref]
  22. H. Barnum, G. Ortiz, R. Somma, and L. Viola, “A generalization of entanglement to convex operational theories: entanglement relative to a subspace of observables,” Int. J. Theor. Phys. 44(12), 2127–2145 (2005).
    [Crossref]
  23. H. Wiseman and J. A. Vaccaro, “Entanglement of Indistinguishable Particles Shared between Two Parties,” Phys. Rev. Lett. 91(9), 097902 (2003).
    [Crossref]
  24. N. Killoran, M. Cramer, and M. B. Plenio, “Extracting Entanglement from Identical Particles,” Phys. Rev. Lett. 112(15), 150501 (2014).
    [Crossref]
  25. A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett. 110(8), 080503 (2013).
    [Crossref]
  26. F. Benatti, R. Floreanini, and U. Marzolino, “Entanglement and squeezing with identical particles: ultracold atom quantum metrology,” J. Phys. B 44(9), 091001 (2011).
    [Crossref]
  27. F. Benatti, R. Floreanini, and U. Marzolino, “Bipartite entanglement in systems of identical particles: the partial transposition criterion,” Ann. Phys. 327(5), 1304–1319 (2012).
    [Crossref]
  28. A. C. Lourenco, T. Debarba, and E. I. Duzzioni, “Entanglement of indistinguishable particles: A comparative study,” Phys. Rev. A 99(1), 012341 (2019).
    [Crossref]
  29. R. L. Franco and G. Compagno, “Quantum Entanglement of Identical Particles by Standard Information-Theoretic Notions,” Sci. Rep. 6(1), 20603 (2016).
    [Crossref]
  30. R. L. Franco and G. Compagno, “Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing,” Phys. Rev. Lett. 120(24), 240403 (2018).
    [Crossref]
  31. G. Compagno, A. Castellini, and R. L. Franco, “Dealing with indistinguishable particles and their entanglement,” Phil. Trans. R. Soc. A 376(2123), 20170317 (2018).
    [Crossref]
  32. S. Chin and J. Huh, “Entanglement of identical particles and coherence in the first quantization language,” Phys. Rev. A 99(5), 052345 (2019).
    [Crossref]
  33. S. Chin and J. Huh, “Reduced density matrix of nonlocal identical particles,” arXiv:1906.00542 (2019).
  34. C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002).
    [Crossref]
  35. N. Paunkovic, The role of indistinguishability of identical particles in quantum information processing, Ph.D. thesis, Oxford university (2004).
  36. M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013).
    [Crossref]
  37. F. Nosrati, A. Castellini, G. Compagno, and R. L. Franco, “Robust entanglement preparation against noise by controlling spatial indistinguishability,” npj Quant. Inf. 6(1), 39 (2020).
    [Crossref]
  38. K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).
  39. B. Dalton, J. Goold, B. Garraway, and M. Reid, “Quantum entanglement for systems of identical bosons: I. General features,” Phys. Scr. 92(2), 023004 (2017).
    [Crossref]
  40. G. C. Wick, A. S. Wightman, and E. P. Wigner, “The Intrinsic Parity of Elementary Particles,” Phys. Rev. 88(1), 101–105 (1952).
    [Crossref]
  41. A. Vaccaro, F. Anselmi, and H. Wiseman, “Entanglement of identical particles and reference phase uncertainty,” Int. J. Quant. Inform. 01(04), 427–441 (2003).
    [Crossref]
  42. S. Hill and W. K. Wootters, “Entanglement of a Pair of Quantum Bits,” Phys. Rev. Lett. 78(26), 5022–5025 (1997).
    [Crossref]
  43. W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80(10), 2245–2248 (1998).
    [Crossref]
  44. Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018).
    [Crossref]
  45. T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
    [Crossref]
  46. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001).
    [Crossref]
  47. T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
    [Crossref]
  48. B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54(15), 4727–4731 (2015).
    [Crossref]
  49. Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8(2), 117–120 (2012).
    [Crossref]
  50. S. Aaronson and A. Arkhipov, inProceedings of the forty- third annual ACM symposium on Theory of computing (ACM, 2011) pp. 333–342.
  51. V. Shchesnovich, “Partial indistinguishability theory for multiphoton experiments in multiport devices,” Phys. Rev. A 91(1), 013844 (2015).
    [Crossref]
  52. M. C. Tichy, “Sampling of partially distinguishable bosons and the relation to the multidimensional permanent,” Phys. Rev. A 91(2), 022316 (2015).
    [Crossref]
  53. S. Chin and J. Huh, “Majorization and the time complexity of linear optical networks,” J. Phys. A: Math. Theor. 52(24), 245301 (2019).
    [Crossref]
  54. G.-C. Wick, A. S. Wightman, and E. P. Wigner, “Superselection Rule for Charge,” Phys. Rev. D 1(12), 3267–3269 (1970).
    [Crossref]
  55. N. Friis, “Reasonable fermionic quantum information theories require relativity,” New J. Phys. 18(3), 033014 (2016).
    [Crossref]
  56. N. Gigena and R. Rossignoli, “Bipartite entanglement in fermion systems,” Phys. Rev. A 95(6), 062320 (2017).
    [Crossref]

2020 (1)

F. Nosrati, A. Castellini, G. Compagno, and R. L. Franco, “Robust entanglement preparation against noise by controlling spatial indistinguishability,” npj Quant. Inf. 6(1), 39 (2020).
[Crossref]

2019 (6)

S. Chin and J. Huh, “Entanglement of identical particles and coherence in the first quantization language,” Phys. Rev. A 99(5), 052345 (2019).
[Crossref]

A. C. Lourenco, T. Debarba, and E. I. Duzzioni, “Entanglement of indistinguishable particles: A comparative study,” Phys. Rev. A 99(1), 012341 (2019).
[Crossref]

V. Balasubramanian, B. Craps, T. De Jonckheere, and G. Sàrosi, “Entanglement versus entwinement in symmetric product orbifolds,” J. High Energy Phys. (online) 2019(1), 190 (2019).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
[Crossref]

S. Chin and J. Huh, “Majorization and the time complexity of linear optical networks,” J. Phys. A: Math. Theor. 52(24), 245301 (2019).
[Crossref]

2018 (3)

Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018).
[Crossref]

R. L. Franco and G. Compagno, “Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing,” Phys. Rev. Lett. 120(24), 240403 (2018).
[Crossref]

G. Compagno, A. Castellini, and R. L. Franco, “Dealing with indistinguishable particles and their entanglement,” Phil. Trans. R. Soc. A 376(2123), 20170317 (2018).
[Crossref]

2017 (2)

B. Dalton, J. Goold, B. Garraway, and M. Reid, “Quantum entanglement for systems of identical bosons: I. General features,” Phys. Scr. 92(2), 023004 (2017).
[Crossref]

N. Gigena and R. Rossignoli, “Bipartite entanglement in fermion systems,” Phys. Rev. A 95(6), 062320 (2017).
[Crossref]

2016 (2)

N. Friis, “Reasonable fermionic quantum information theories require relativity,” New J. Phys. 18(3), 033014 (2016).
[Crossref]

R. L. Franco and G. Compagno, “Quantum Entanglement of Identical Particles by Standard Information-Theoretic Notions,” Sci. Rep. 6(1), 20603 (2016).
[Crossref]

2015 (3)

V. Shchesnovich, “Partial indistinguishability theory for multiphoton experiments in multiport devices,” Phys. Rev. A 91(1), 013844 (2015).
[Crossref]

M. C. Tichy, “Sampling of partially distinguishable bosons and the relation to the multidimensional permanent,” Phys. Rev. A 91(2), 022316 (2015).
[Crossref]

B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54(15), 4727–4731 (2015).
[Crossref]

2014 (1)

N. Killoran, M. Cramer, and M. B. Plenio, “Extracting Entanglement from Identical Particles,” Phys. Rev. Lett. 112(15), 150501 (2014).
[Crossref]

2013 (3)

A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett. 110(8), 080503 (2013).
[Crossref]

M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013).
[Crossref]

A. Balachandran, T. Govindarajan, A. R. de Queiroz, and A. Reyes-Lega, “Algebraic approach to entanglement and entropy,” Phys. Rev. A 88(2), 022301 (2013).
[Crossref]

2012 (2)

F. Benatti, R. Floreanini, and U. Marzolino, “Bipartite entanglement in systems of identical particles: the partial transposition criterion,” Ann. Phys. 327(5), 1304–1319 (2012).
[Crossref]

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8(2), 117–120 (2012).
[Crossref]

2011 (1)

F. Benatti, R. Floreanini, and U. Marzolino, “Entanglement and squeezing with identical particles: ultracold atom quantum metrology,” J. Phys. B 44(9), 091001 (2011).
[Crossref]

2010 (1)

T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
[Crossref]

2005 (1)

H. Barnum, G. Ortiz, R. Somma, and L. Viola, “A generalization of entanglement to convex operational theories: entanglement relative to a subspace of observables,” Int. J. Theor. Phys. 44(12), 2127–2145 (2005).
[Crossref]

2004 (1)

H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004).
[Crossref]

2003 (3)

A. Vaccaro, F. Anselmi, and H. Wiseman, “Entanglement of identical particles and reference phase uncertainty,” Int. J. Quant. Inform. 01(04), 427–441 (2003).
[Crossref]

H. Wiseman and J. A. Vaccaro, “Entanglement of Indistinguishable Particles Shared between Two Parties,” Phys. Rev. Lett. 91(9), 097902 (2003).
[Crossref]

Y. Shi, “Quantum entanglement of identical particles,” Phys. Rev. A 67(2), 024301 (2003).
[Crossref]

2002 (5)

P. Zanardi, “Quantum entanglement in fermionic lattices,” Phys. Rev. A 65(4), 042101 (2002).
[Crossref]

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

G. Ghirardi, L. Marinatto, and T. Weber, “Entanglement and Properties of Composite Quantum Systems: a Conceptual and Mathematical Analysis,” J. Stat. Phys. 108(1/2), 49–122 (2002).
[Crossref]

K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, “Quantum Correlations in Systems of Indistinguishable Particles,” Ann. Phys. 299(1), 88–127 (2002).
[Crossref]

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002).
[Crossref]

2001 (4)

R. Paskauskas and L. You, “Quantum correlations in two-boson wave functions,” Phys. Rev. A 64(4), 042310 (2001).
[Crossref]

J. Schliemann, D. Loss, and A. H. MacDonald, “Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots,” Phys. Rev. B 63(8), 085311 (2001).
[Crossref]

J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001).
[Crossref]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001).
[Crossref]

1998 (1)

W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80(10), 2245–2248 (1998).
[Crossref]

1997 (1)

S. Hill and W. K. Wootters, “Entanglement of a Pair of Quantum Bits,” Phys. Rev. Lett. 78(26), 5022–5025 (1997).
[Crossref]

1993 (1)

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
[Crossref]

1977 (1)

G. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,” Nuovo Cim. B 39(1), 130–134 (1977).
[Crossref]

1970 (1)

G.-C. Wick, A. S. Wightman, and E. P. Wigner, “Superselection Rule for Charge,” Phys. Rev. D 1(12), 3267–3269 (1970).
[Crossref]

1952 (1)

G. C. Wick, A. S. Wightman, and E. P. Wigner, “The Intrinsic Parity of Elementary Particles,” Phys. Rev. 88(1), 101–105 (1952).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47(10), 777–780 (1935).
[Crossref]

Aaronson, S.

S. Aaronson and A. Arkhipov, inProceedings of the forty- third annual ACM symposium on Theory of computing (ACM, 2011) pp. 333–342.

Anselmi, F.

A. Vaccaro, F. Anselmi, and H. Wiseman, “Entanglement of identical particles and reference phase uncertainty,” Int. J. Quant. Inform. 01(04), 427–441 (2003).
[Crossref]

Arkhipov, A.

S. Aaronson and A. Arkhipov, inProceedings of the forty- third annual ACM symposium on Theory of computing (ACM, 2011) pp. 333–342.

Balachandran, A.

A. Balachandran, T. Govindarajan, A. R. de Queiroz, and A. Reyes-Lega, “Algebraic approach to entanglement and entropy,” Phys. Rev. A 88(2), 022301 (2013).
[Crossref]

Balachandran, A. P.

A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett. 110(8), 080503 (2013).
[Crossref]

Balasubramanian, V.

V. Balasubramanian, B. Craps, T. De Jonckheere, and G. Sàrosi, “Entanglement versus entwinement in symmetric product orbifolds,” J. High Energy Phys. (online) 2019(1), 190 (2019).
[Crossref]

Barnum, H.

H. Barnum, G. Ortiz, R. Somma, and L. Viola, “A generalization of entanglement to convex operational theories: entanglement relative to a subspace of observables,” Int. J. Theor. Phys. 44(12), 2127–2145 (2005).
[Crossref]

H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004).
[Crossref]

Bell, J. S.

J. S. Bell, Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy (Cambridge university, 2004).

Benatti, F.

F. Benatti, R. Floreanini, and U. Marzolino, “Bipartite entanglement in systems of identical particles: the partial transposition criterion,” Ann. Phys. 327(5), 1304–1319 (2012).
[Crossref]

F. Benatti, R. Floreanini, and U. Marzolino, “Entanglement and squeezing with identical particles: ultracold atom quantum metrology,” J. Phys. B 44(9), 091001 (2011).
[Crossref]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

Brambilla, E.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

Bruss, D.

K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, “Quantum Correlations in Systems of Indistinguishable Particles,” Ann. Phys. 299(1), 88–127 (2002).
[Crossref]

Buchleitner, A.

M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013).
[Crossref]

Castellini, A.

F. Nosrati, A. Castellini, G. Compagno, and R. L. Franco, “Robust entanglement preparation against noise by controlling spatial indistinguishability,” npj Quant. Inf. 6(1), 39 (2020).
[Crossref]

G. Compagno, A. Castellini, and R. L. Franco, “Dealing with indistinguishable particles and their entanglement,” Phil. Trans. R. Soc. A 376(2123), 20170317 (2018).
[Crossref]

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Chin, S.

S. Chin and J. Huh, “Entanglement of identical particles and coherence in the first quantization language,” Phys. Rev. A 99(5), 052345 (2019).
[Crossref]

S. Chin and J. Huh, “Majorization and the time complexity of linear optical networks,” J. Phys. A: Math. Theor. 52(24), 245301 (2019).
[Crossref]

S. Chin and J. Huh, “Reduced density matrix of nonlocal identical particles,” arXiv:1906.00542 (2019).

S. Chin and J.-H. Chun, “Taming identical particles for discerning the genuine nonlocality,” arXiv:2002.03784 (2020).

Cho, Y.-W.

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
[Crossref]

Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018).
[Crossref]

Chun, J.-H.

S. Chin and J.-H. Chun, “Taming identical particles for discerning the genuine nonlocality,” arXiv:2002.03784 (2020).

Cirac, J. I.

J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001).
[Crossref]

Compagno, G.

F. Nosrati, A. Castellini, G. Compagno, and R. L. Franco, “Robust entanglement preparation against noise by controlling spatial indistinguishability,” npj Quant. Inf. 6(1), 39 (2020).
[Crossref]

R. L. Franco and G. Compagno, “Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing,” Phys. Rev. Lett. 120(24), 240403 (2018).
[Crossref]

G. Compagno, A. Castellini, and R. L. Franco, “Dealing with indistinguishable particles and their entanglement,” Phil. Trans. R. Soc. A 376(2123), 20170317 (2018).
[Crossref]

R. L. Franco and G. Compagno, “Quantum Entanglement of Identical Particles by Standard Information-Theoretic Notions,” Sci. Rep. 6(1), 20603 (2016).
[Crossref]

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Cramer, M.

N. Killoran, M. Cramer, and M. B. Plenio, “Extracting Entanglement from Identical Particles,” Phys. Rev. Lett. 112(15), 150501 (2014).
[Crossref]

Craps, B.

V. Balasubramanian, B. Craps, T. De Jonckheere, and G. Sàrosi, “Entanglement versus entwinement in symmetric product orbifolds,” J. High Energy Phys. (online) 2019(1), 190 (2019).
[Crossref]

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

Dalton, B.

B. Dalton, J. Goold, B. Garraway, and M. Reid, “Quantum entanglement for systems of identical bosons: I. General features,” Phys. Scr. 92(2), 023004 (2017).
[Crossref]

De Jonckheere, T.

V. Balasubramanian, B. Craps, T. De Jonckheere, and G. Sàrosi, “Entanglement versus entwinement in symmetric product orbifolds,” J. High Energy Phys. (online) 2019(1), 190 (2019).
[Crossref]

de Melo, F.

M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013).
[Crossref]

de Queiroz, A. R.

A. Balachandran, T. Govindarajan, A. R. de Queiroz, and A. Reyes-Lega, “Algebraic approach to entanglement and entropy,” Phys. Rev. A 88(2), 022301 (2013).
[Crossref]

A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett. 110(8), 080503 (2013).
[Crossref]

Debarba, T.

A. C. Lourenco, T. Debarba, and E. I. Duzzioni, “Entanglement of indistinguishable particles: A comparative study,” Phys. Rev. A 99(1), 012341 (2019).
[Crossref]

Dirac, P. A. M.

P. A. M. Dirac, The principles of quantum mechanics (Oxford university, 1981).

Duzzioni, E. I.

A. C. Lourenco, T. Debarba, and E. I. Duzzioni, “Entanglement of indistinguishable particles: A comparative study,” Phys. Rev. A 99(1), 012341 (2019).
[Crossref]

Eckert, K.

K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, “Quantum Correlations in Systems of Indistinguishable Particles,” Ann. Phys. 299(1), 88–127 (2002).
[Crossref]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47(10), 777–780 (1935).
[Crossref]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
[Crossref]

Floreanini, R.

F. Benatti, R. Floreanini, and U. Marzolino, “Bipartite entanglement in systems of identical particles: the partial transposition criterion,” Ann. Phys. 327(5), 1304–1319 (2012).
[Crossref]

F. Benatti, R. Floreanini, and U. Marzolino, “Entanglement and squeezing with identical particles: ultracold atom quantum metrology,” J. Phys. B 44(9), 091001 (2011).
[Crossref]

Franco, R. L.

F. Nosrati, A. Castellini, G. Compagno, and R. L. Franco, “Robust entanglement preparation against noise by controlling spatial indistinguishability,” npj Quant. Inf. 6(1), 39 (2020).
[Crossref]

R. L. Franco and G. Compagno, “Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing,” Phys. Rev. Lett. 120(24), 240403 (2018).
[Crossref]

G. Compagno, A. Castellini, and R. L. Franco, “Dealing with indistinguishable particles and their entanglement,” Phil. Trans. R. Soc. A 376(2123), 20170317 (2018).
[Crossref]

R. L. Franco and G. Compagno, “Quantum Entanglement of Identical Particles by Standard Information-Theoretic Notions,” Sci. Rep. 6(1), 20603 (2016).
[Crossref]

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Friis, N.

N. Friis, “Reasonable fermionic quantum information theories require relativity,” New J. Phys. 18(3), 033014 (2016).
[Crossref]

Garraway, B.

B. Dalton, J. Goold, B. Garraway, and M. Reid, “Quantum entanglement for systems of identical bosons: I. General features,” Phys. Scr. 92(2), 023004 (2017).
[Crossref]

Gatti, A.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

Ghirardi, G.

G. Ghirardi, L. Marinatto, and T. Weber, “Entanglement and Properties of Composite Quantum Systems: a Conceptual and Mathematical Analysis,” J. Stat. Phys. 108(1/2), 49–122 (2002).
[Crossref]

G. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,” Nuovo Cim. B 39(1), 130–134 (1977).
[Crossref]

Gigena, N.

N. Gigena and R. Rossignoli, “Bipartite entanglement in fermion systems,” Phys. Rev. A 95(6), 062320 (2017).
[Crossref]

Goold, J.

B. Dalton, J. Goold, B. Garraway, and M. Reid, “Quantum entanglement for systems of identical bosons: I. General features,” Phys. Scr. 92(2), 023004 (2017).
[Crossref]

Govindarajan, T.

A. Balachandran, T. Govindarajan, A. R. de Queiroz, and A. Reyes-Lega, “Algebraic approach to entanglement and entropy,” Phys. Rev. A 88(2), 022301 (2013).
[Crossref]

Govindarajan, T. R.

A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett. 110(8), 080503 (2013).
[Crossref]

Guo, G.-C.

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Han, S.-W.

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
[Crossref]

Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018).
[Crossref]

B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54(15), 4727–4731 (2015).
[Crossref]

Hill, S.

S. Hill and W. K. Wootters, “Entanglement of a Pair of Quantum Bits,” Phys. Rev. Lett. 78(26), 5022–5025 (1997).
[Crossref]

Huh, J.

S. Chin and J. Huh, “Entanglement of identical particles and coherence in the first quantization language,” Phys. Rev. A 99(5), 052345 (2019).
[Crossref]

S. Chin and J. Huh, “Majorization and the time complexity of linear optical networks,” J. Phys. A: Math. Theor. 52(24), 245301 (2019).
[Crossref]

S. Chin and J. Huh, “Reduced density matrix of nonlocal identical particles,” arXiv:1906.00542 (2019).

James, D. F. V.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001).
[Crossref]

Jelezko, F.

T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
[Crossref]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

Kang, M.-S.

Killoran, N.

N. Killoran, M. Cramer, and M. B. Plenio, “Extracting Entanglement from Identical Particles,” Phys. Rev. Lett. 112(15), 150501 (2014).
[Crossref]

Kim, Y.-H.

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8(2), 117–120 (2012).
[Crossref]

Kim, Y.-S.

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
[Crossref]

Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018).
[Crossref]

B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54(15), 4727–4731 (2015).
[Crossref]

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8(2), 117–120 (2012).
[Crossref]

Knill, E.

H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004).
[Crossref]

Kus, M.

M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013).
[Crossref]

J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001).
[Crossref]

Kwiat, P. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001).
[Crossref]

Kwon, O.

B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54(15), 4727–4731 (2015).
[Crossref]

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8(2), 117–120 (2012).
[Crossref]

Ladd, T.

T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
[Crossref]

Laflamme, R.

T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
[Crossref]

Lee, J.-C.

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8(2), 117–120 (2012).
[Crossref]

Lee, S.-Y.

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
[Crossref]

Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018).
[Crossref]

Lewenstein, M.

K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, “Quantum Correlations in Systems of Indistinguishable Particles,” Ann. Phys. 299(1), 88–127 (2002).
[Crossref]

J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001).
[Crossref]

Li, C.-F.

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Liu, Z.-H.

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Loss, D.

J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001).
[Crossref]

J. Schliemann, D. Loss, and A. H. MacDonald, “Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots,” Phys. Rev. B 63(8), 085311 (2001).
[Crossref]

Lourenco, A. C.

A. C. Lourenco, T. Debarba, and E. I. Duzzioni, “Entanglement of indistinguishable particles: A comparative study,” Phys. Rev. A 99(1), 012341 (2019).
[Crossref]

Lugiato, L.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

MacDonald, A. H.

J. Schliemann, D. Loss, and A. H. MacDonald, “Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots,” Phys. Rev. B 63(8), 085311 (2001).
[Crossref]

Marinatto, L.

G. Ghirardi, L. Marinatto, and T. Weber, “Entanglement and Properties of Composite Quantum Systems: a Conceptual and Mathematical Analysis,” J. Stat. Phys. 108(1/2), 49–122 (2002).
[Crossref]

Marzolino, U.

F. Benatti, R. Floreanini, and U. Marzolino, “Bipartite entanglement in systems of identical particles: the partial transposition criterion,” Ann. Phys. 327(5), 1304–1319 (2012).
[Crossref]

F. Benatti, R. Floreanini, and U. Marzolino, “Entanglement and squeezing with identical particles: ultracold atom quantum metrology,” J. Phys. B 44(9), 091001 (2011).
[Crossref]

Mintert, F.

M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013).
[Crossref]

Monroe, C.

T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
[Crossref]

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002).
[Crossref]

Moon, S.

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
[Crossref]

Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018).
[Crossref]

B. K. Park, Y.-S. Kim, O. Kwon, S.-W. Han, and S. Moon, “High-performance reconfigurable coincidence counting unit based on a field programmable gate array,” Appl. Opt. 54(15), 4727–4731 (2015).
[Crossref]

Munro, W. J.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001).
[Crossref]

Nakamura, Y.

T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
[Crossref]

Nosrati, F.

F. Nosrati, A. Castellini, G. Compagno, and R. L. Franco, “Robust entanglement preparation against noise by controlling spatial indistinguishability,” npj Quant. Inf. 6(1), 39 (2020).
[Crossref]

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

O’Brien, J. L.

T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
[Crossref]

Omero, C.

G. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,” Nuovo Cim. B 39(1), 130–134 (1977).
[Crossref]

Ortiz, G.

H. Barnum, G. Ortiz, R. Somma, and L. Viola, “A generalization of entanglement to convex operational theories: entanglement relative to a subspace of observables,” Int. J. Theor. Phys. 44(12), 2127–2145 (2005).
[Crossref]

H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004).
[Crossref]

Park, B. K.

Paskauskas, R.

R. Paskauskas and L. You, “Quantum correlations in two-boson wave functions,” Phys. Rev. A 64(4), 042310 (2001).
[Crossref]

Paunkovic, N.

N. Paunkovic, The role of indistinguishability of identical particles in quantum information processing, Ph.D. thesis, Oxford university (2004).

Peres, A.

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

A. Peres, Quantum theory: concepts and methods, Vol. 57 (Springer, 2006).

Plenio, M. B.

N. Killoran, M. Cramer, and M. B. Plenio, “Extracting Entanglement from Identical Particles,” Phys. Rev. Lett. 112(15), 150501 (2014).
[Crossref]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47(10), 777–780 (1935).
[Crossref]

Pramanik, T.

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
[Crossref]

Y.-S. Kim, T. Pramanik, Y.-W. Cho, M. Yang, S.-W. Han, S.-Y. Lee, M.-S. Kang, and S. Moon, “Informationally symmetrical Bell state preparation and measurement,” Opt. Express 26(22), 29539–29549 (2018).
[Crossref]

Reid, M.

B. Dalton, J. Goold, B. Garraway, and M. Reid, “Quantum entanglement for systems of identical bosons: I. General features,” Phys. Scr. 92(2), 023004 (2017).
[Crossref]

Reyes-Lega, A.

A. Balachandran, T. Govindarajan, A. R. de Queiroz, and A. Reyes-Lega, “Algebraic approach to entanglement and entropy,” Phys. Rev. A 88(2), 022301 (2013).
[Crossref]

Reyes-Lega, A. F.

A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett. 110(8), 080503 (2013).
[Crossref]

Rimini, A.

G. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,” Nuovo Cim. B 39(1), 130–134 (1977).
[Crossref]

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47(10), 777–780 (1935).
[Crossref]

Rossignoli, R.

N. Gigena and R. Rossignoli, “Bipartite entanglement in fermion systems,” Phys. Rev. A 95(6), 062320 (2017).
[Crossref]

Sàrosi, G.

V. Balasubramanian, B. Craps, T. De Jonckheere, and G. Sàrosi, “Entanglement versus entwinement in symmetric product orbifolds,” J. High Energy Phys. (online) 2019(1), 190 (2019).
[Crossref]

Schliemann, J.

K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, “Quantum Correlations in Systems of Indistinguishable Particles,” Ann. Phys. 299(1), 88–127 (2002).
[Crossref]

J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001).
[Crossref]

J. Schliemann, D. Loss, and A. H. MacDonald, “Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots,” Phys. Rev. B 63(8), 085311 (2001).
[Crossref]

Schrödinger, E.

E. Schrödinger, in Mathematical Proceedings of the Cam- bridge Philosophical Society, 31555–563 (1935).

Shchesnovich, V.

V. Shchesnovich, “Partial indistinguishability theory for multiphoton experiments in multiport devices,” Phys. Rev. A 91(1), 013844 (2015).
[Crossref]

Shi, Y.

Y. Shi, “Quantum entanglement of identical particles,” Phys. Rev. A 67(2), 024301 (2003).
[Crossref]

Somma, R.

H. Barnum, G. Ortiz, R. Somma, and L. Viola, “A generalization of entanglement to convex operational theories: entanglement relative to a subspace of observables,” Int. J. Theor. Phys. 44(12), 2127–2145 (2005).
[Crossref]

H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004).
[Crossref]

Sun, K.

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Tichy, M. C.

M. C. Tichy, “Sampling of partially distinguishable bosons and the relation to the multidimensional permanent,” Phys. Rev. A 91(2), 022316 (2015).
[Crossref]

M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013).
[Crossref]

Vaccaro, A.

A. Vaccaro, F. Anselmi, and H. Wiseman, “Entanglement of identical particles and reference phase uncertainty,” Int. J. Quant. Inform. 01(04), 427–441 (2003).
[Crossref]

Vaccaro, J. A.

H. Wiseman and J. A. Vaccaro, “Entanglement of Indistinguishable Particles Shared between Two Parties,” Phys. Rev. Lett. 91(9), 097902 (2003).
[Crossref]

Viola, L.

H. Barnum, G. Ortiz, R. Somma, and L. Viola, “A generalization of entanglement to convex operational theories: entanglement relative to a subspace of observables,” Int. J. Theor. Phys. 44(12), 2127–2145 (2005).
[Crossref]

H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004).
[Crossref]

Wang, Y.

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Weber, T.

G. Ghirardi, L. Marinatto, and T. Weber, “Entanglement and Properties of Composite Quantum Systems: a Conceptual and Mathematical Analysis,” J. Stat. Phys. 108(1/2), 49–122 (2002).
[Crossref]

G. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,” Nuovo Cim. B 39(1), 130–134 (1977).
[Crossref]

White, A. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001).
[Crossref]

Wick, G. C.

G. C. Wick, A. S. Wightman, and E. P. Wigner, “The Intrinsic Parity of Elementary Particles,” Phys. Rev. 88(1), 101–105 (1952).
[Crossref]

Wick, G.-C.

G.-C. Wick, A. S. Wightman, and E. P. Wigner, “Superselection Rule for Charge,” Phys. Rev. D 1(12), 3267–3269 (1970).
[Crossref]

Wightman, A. S.

G.-C. Wick, A. S. Wightman, and E. P. Wigner, “Superselection Rule for Charge,” Phys. Rev. D 1(12), 3267–3269 (1970).
[Crossref]

G. C. Wick, A. S. Wightman, and E. P. Wigner, “The Intrinsic Parity of Elementary Particles,” Phys. Rev. 88(1), 101–105 (1952).
[Crossref]

Wigner, E. P.

G.-C. Wick, A. S. Wightman, and E. P. Wigner, “Superselection Rule for Charge,” Phys. Rev. D 1(12), 3267–3269 (1970).
[Crossref]

G. C. Wick, A. S. Wightman, and E. P. Wigner, “The Intrinsic Parity of Elementary Particles,” Phys. Rev. 88(1), 101–105 (1952).
[Crossref]

Wiseman, H.

A. Vaccaro, F. Anselmi, and H. Wiseman, “Entanglement of identical particles and reference phase uncertainty,” Int. J. Quant. Inform. 01(04), 427–441 (2003).
[Crossref]

H. Wiseman and J. A. Vaccaro, “Entanglement of Indistinguishable Particles Shared between Two Parties,” Phys. Rev. Lett. 91(9), 097902 (2003).
[Crossref]

Wootters, W. K.

W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80(10), 2245–2248 (1998).
[Crossref]

S. Hill and W. K. Wootters, “Entanglement of a Pair of Quantum Bits,” Phys. Rev. Lett. 78(26), 5022–5025 (1997).
[Crossref]

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

Xu, J.-S.

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Xu, X.-Y.

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

Yang, M.

You, L.

R. Paskauskas and L. You, “Quantum correlations in two-boson wave functions,” Phys. Rev. A 64(4), 042310 (2001).
[Crossref]

Zanardi, P.

P. Zanardi, “Quantum entanglement in fermionic lattices,” Phys. Rev. A 65(4), 042101 (2002).
[Crossref]

Ann. Phys. (2)

K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, “Quantum Correlations in Systems of Indistinguishable Particles,” Ann. Phys. 299(1), 88–127 (2002).
[Crossref]

F. Benatti, R. Floreanini, and U. Marzolino, “Bipartite entanglement in systems of identical particles: the partial transposition criterion,” Ann. Phys. 327(5), 1304–1319 (2012).
[Crossref]

Appl. Opt. (1)

Fortschr. Phys. (1)

M. C. Tichy, F. de Melo, M. Kus, F. Mintert, and A. Buchleitner, “Entanglement of identical particles and the detection process,” Fortschr. Phys. 61(2-3), 225–237 (2013).
[Crossref]

Int. J. Quant. Inform. (1)

A. Vaccaro, F. Anselmi, and H. Wiseman, “Entanglement of identical particles and reference phase uncertainty,” Int. J. Quant. Inform. 01(04), 427–441 (2003).
[Crossref]

Int. J. Theor. Phys. (1)

H. Barnum, G. Ortiz, R. Somma, and L. Viola, “A generalization of entanglement to convex operational theories: entanglement relative to a subspace of observables,” Int. J. Theor. Phys. 44(12), 2127–2145 (2005).
[Crossref]

J. High Energy Phys. (online) (1)

V. Balasubramanian, B. Craps, T. De Jonckheere, and G. Sàrosi, “Entanglement versus entwinement in symmetric product orbifolds,” J. High Energy Phys. (online) 2019(1), 190 (2019).
[Crossref]

J. Opt. B: Quantum Semiclassical Opt. (1)

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum Semiclassical Opt. 4(3), S176–S183 (2002).
[Crossref]

J. Phys. A: Math. Theor. (1)

S. Chin and J. Huh, “Majorization and the time complexity of linear optical networks,” J. Phys. A: Math. Theor. 52(24), 245301 (2019).
[Crossref]

J. Phys. B (1)

F. Benatti, R. Floreanini, and U. Marzolino, “Entanglement and squeezing with identical particles: ultracold atom quantum metrology,” J. Phys. B 44(9), 091001 (2011).
[Crossref]

J. Stat. Phys. (1)

G. Ghirardi, L. Marinatto, and T. Weber, “Entanglement and Properties of Composite Quantum Systems: a Conceptual and Mathematical Analysis,” J. Stat. Phys. 108(1/2), 49–122 (2002).
[Crossref]

Nat. Phys. (1)

Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, “Protecting entanglement from decoherence using weak measurement and quantum measurement reversal,” Nat. Phys. 8(2), 117–120 (2012).
[Crossref]

Nature (2)

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002).
[Crossref]

T. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum Computers,” Nature 464(7285), 45–53 (2010).
[Crossref]

New J. Phys. (1)

N. Friis, “Reasonable fermionic quantum information theories require relativity,” New J. Phys. 18(3), 033014 (2016).
[Crossref]

npj Quant. Inf. (1)

F. Nosrati, A. Castellini, G. Compagno, and R. L. Franco, “Robust entanglement preparation against noise by controlling spatial indistinguishability,” npj Quant. Inf. 6(1), 39 (2020).
[Crossref]

Nuovo Cim. B (1)

G. Ghirardi, A. Rimini, T. Weber, and C. Omero, “Some simple remarks about quantum nonseparability for systems composed of identical constituents,” Nuovo Cim. B 39(1), 130–134 (1977).
[Crossref]

Opt. Express (1)

Phil. Trans. R. Soc. A (1)

G. Compagno, A. Castellini, and R. L. Franco, “Dealing with indistinguishable particles and their entanglement,” Phil. Trans. R. Soc. A 376(2123), 20170317 (2018).
[Crossref]

Phys. Rev. (2)

A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47(10), 777–780 (1935).
[Crossref]

G. C. Wick, A. S. Wightman, and E. P. Wigner, “The Intrinsic Parity of Elementary Particles,” Phys. Rev. 88(1), 101–105 (1952).
[Crossref]

Phys. Rev. A (13)

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, Y.-S. Kim, and S. Moon, “Revealing hidden quantum steerability using local filtering operations,” Phys. Rev. A 99(3), 030101 (2019).
[Crossref]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001).
[Crossref]

T. Pramanik, Y.-W. Cho, S.-W. Han, S.-Y. Lee, S. Moon, and Y.-S. Kim, “Nonlocal quantum correlations under amplitude damping decoherence,” Phys. Rev. A 100(4), 042311 (2019).
[Crossref]

N. Gigena and R. Rossignoli, “Bipartite entanglement in fermion systems,” Phys. Rev. A 95(6), 062320 (2017).
[Crossref]

V. Shchesnovich, “Partial indistinguishability theory for multiphoton experiments in multiport devices,” Phys. Rev. A 91(1), 013844 (2015).
[Crossref]

M. C. Tichy, “Sampling of partially distinguishable bosons and the relation to the multidimensional permanent,” Phys. Rev. A 91(2), 022316 (2015).
[Crossref]

A. Balachandran, T. Govindarajan, A. R. de Queiroz, and A. Reyes-Lega, “Algebraic approach to entanglement and entropy,” Phys. Rev. A 88(2), 022301 (2013).
[Crossref]

R. Paskauskas and L. You, “Quantum correlations in two-boson wave functions,” Phys. Rev. A 64(4), 042310 (2001).
[Crossref]

P. Zanardi, “Quantum entanglement in fermionic lattices,” Phys. Rev. A 65(4), 042101 (2002).
[Crossref]

Y. Shi, “Quantum entanglement of identical particles,” Phys. Rev. A 67(2), 024301 (2003).
[Crossref]

S. Chin and J. Huh, “Entanglement of identical particles and coherence in the first quantization language,” Phys. Rev. A 99(5), 052345 (2019).
[Crossref]

A. C. Lourenco, T. Debarba, and E. I. Duzzioni, “Entanglement of indistinguishable particles: A comparative study,” Phys. Rev. A 99(1), 012341 (2019).
[Crossref]

J. Schliemann, J. I. Cirac, M. Kus, M. Lewenstein, and D. Loss, “Quantum correlations in two-fermion systems,” Phys. Rev. A 64(2), 022303 (2001).
[Crossref]

Phys. Rev. B (1)

J. Schliemann, D. Loss, and A. H. MacDonald, “Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots,” Phys. Rev. B 63(8), 085311 (2001).
[Crossref]

Phys. Rev. D (1)

G.-C. Wick, A. S. Wightman, and E. P. Wigner, “Superselection Rule for Charge,” Phys. Rev. D 1(12), 3267–3269 (1970).
[Crossref]

Phys. Rev. Lett. (9)

S. Hill and W. K. Wootters, “Entanglement of a Pair of Quantum Bits,” Phys. Rev. Lett. 78(26), 5022–5025 (1997).
[Crossref]

W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80(10), 2245–2248 (1998).
[Crossref]

R. L. Franco and G. Compagno, “Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing,” Phys. Rev. Lett. 120(24), 240403 (2018).
[Crossref]

H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, “A Subsystem-Independent Generalization of Entanglement,” Phys. Rev. Lett. 92(10), 107902 (2004).
[Crossref]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
[Crossref]

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

H. Wiseman and J. A. Vaccaro, “Entanglement of Indistinguishable Particles Shared between Two Parties,” Phys. Rev. Lett. 91(9), 097902 (2003).
[Crossref]

N. Killoran, M. Cramer, and M. B. Plenio, “Extracting Entanglement from Identical Particles,” Phys. Rev. Lett. 112(15), 150501 (2014).
[Crossref]

A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, “Entanglement and Particle Identity: A Unifying Approach,” Phys. Rev. Lett. 110(8), 080503 (2013).
[Crossref]

Phys. Scr. (1)

B. Dalton, J. Goold, B. Garraway, and M. Reid, “Quantum entanglement for systems of identical bosons: I. General features,” Phys. Scr. 92(2), 023004 (2017).
[Crossref]

Sci. Rep. (1)

R. L. Franco and G. Compagno, “Quantum Entanglement of Identical Particles by Standard Information-Theoretic Notions,” Sci. Rep. 6(1), 20603 (2016).
[Crossref]

Other (9)

S. Chin and J. Huh, “Reduced density matrix of nonlocal identical particles,” arXiv:1906.00542 (2019).

K. Sun, Y. Wang, Z.-H. Liu, X.-Y. Xu, J.-S. Xu, C.-F. Li, G.-C. Guo, A. Castellini, F. Nosrati, G. Compagno, and R. L. Franco, “Experimental control of remote spatial indistinguishability of photons to realize entanglement and teleportation,” arXiv:2003.10659 (2020).

N. Paunkovic, The role of indistinguishability of identical particles in quantum information processing, Ph.D. thesis, Oxford university (2004).

J. S. Bell, Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy (Cambridge university, 2004).

E. Schrödinger, in Mathematical Proceedings of the Cam- bridge Philosophical Society, 31555–563 (1935).

P. A. M. Dirac, The principles of quantum mechanics (Oxford university, 1981).

A. Peres, Quantum theory: concepts and methods, Vol. 57 (Springer, 2006).

S. Chin and J.-H. Chun, “Taming identical particles for discerning the genuine nonlocality,” arXiv:2002.03784 (2020).

S. Aaronson and A. Arkhipov, inProceedings of the forty- third annual ACM symposium on Theory of computing (ACM, 2011) pp. 333–342.

Supplementary Material (1)

NameDescription
» Supplement 1       Details of theory

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Generic setup for detecting entanglement of two identical particles: The spatially overlapped particles have internal spins ($\uparrow$ and $\downarrow$) and distinguishability (represented as two different colors, red and blue, in the figure). Two detectors located at $L$ and $R$ indicate the spins of the particles.
Fig. 2.
Fig. 2. The experimental setup to entangling photons via their spatial overlap and indistinguishability. Pol. : polarizer, H$^{*}$ : half waveplate at $\theta$, BD : beam displacer, H$_{45}$ : half waveplate at 45$^{\circ }$, WP : waveplates, PBS : polarizing beamsplitter, D1-D4 : single photon detectors, CCU : coincidence counting unit. The optical delay $l$ of a photon has been scanned in order to introduce the particle indistinguishability.
Fig. 3.
Fig. 3. Coincidence counts with respect to scanning the optical delay. A HOM dip can be observed for the coincidences D12 (experimental data and fitting curve in red) and D34 (experimental data and fitting curve in blue), the visibilities were $V=0.99\pm 0.04$ and $V=0.91\pm 0.05$, respectively. The error bars represent one standard deviation due to Poissonian counting statistics.
Fig. 4.
Fig. 4. Concurrence with respect to (a) particle distinguishability, and (b) spatial overlap, respectively. The particle distinguishability is adjusted by the optical delay $l$, and the spatial overlap is controlled by the angle $\theta$ of the H$_{\theta }$. The error bars present the one standard deviation from 100 reconstructed two-qubit states $\rho _{\textrm {ex}}$ by taking into account the Poisson statistics in measured coincidence counts.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

| Ψ = | Ψ A , Ψ B ,
| Ψ A , Ψ B = | Ψ B , Ψ A .
Ψ C , Ψ D | Ψ A , Ψ B = Ψ C | Ψ A Ψ D | Ψ B + Ψ C | Ψ B Ψ D | Ψ A , Ψ C | Ψ A , Ψ B = 1 2 [ Ψ C | Ψ A | Ψ B + Ψ C | Ψ B | Ψ A ] .
| Ψ = | ( ψ A , , ϕ A ) , ( ψ B , , ϕ B ) .
E P ( | Ψ ) = N p N E ( | Ψ N ) ,
| ψ A = α l | L + α r | R , | ψ B = β l | L + β r | R ,
| Ψ = α l β l | ( L , , ϕ A ) , ( L , , ϕ B ) + α l β r | ( L , , ϕ A ) , ( R , , ϕ B ) + α r β l | ( L , , ϕ B ) , ( R , , ϕ A ) + α r β r | ( R , , ϕ A ) , ( R , , ϕ B ) .
a ϕ | X a X a | ϕ = 1
ρ ( 1 , 1 ) m = a , b ( L , X a ) , ( R , X b ) | Ψ Ψ | ( L , X a ) , ( R , X b ) .
( L , X a ) , ( R , X b ) | ( L , , ϕ 1 ) , ( R , , ϕ 2 ) = X a | ϕ 1 X b | ϕ 2 | ( L , ) , ( R , ) ,
ρ ( 1 , 1 ) m = | α l β r | 2 | ( L , ) , ( R , ) ( L , ) , ( R , ) | + | α r β l | 2 | ( L , ) , ( R , ) ( L , ) , ( R , ) | + α l β r α r β l | ϕ 1 | ϕ 2 | 2 | ( L , ) , ( R , ) ( L , ) , ( R , ) | + α l β r α r β l | ϕ 1 | ϕ 2 | 2 | ( L , ) , ( R , ) ( L , ) , ( R , ) | .
C = 4 | α l α r β l β l | | ϕ A | ϕ B | 2 .
4 | α L α R β L β R | = sin 2 4 θ .
C = sin 2 4 θ exp [ l 2 2 σ 2 ] .

Metrics