Abstract

Einstein-Podolsky-Rosen steering is an intermediate relationship between entanglement and Bell nonlocality in the hierarchical structure of quantum nonlocality. To certify the steerability of the entangled state, Mermin steering inequality is supposed to be violated by exceeding the inequality bound of 2. We present an experimental generation of post-selected three-photon entangled states and witness a maximal violation of the inequality up to 3.50±0.05. In the context of observing the maximal violation of Mermin steering inequality which requires measuring on the GHZ state, we derive a tight lower bound on the GHZ-fidelity that can be certified from the Mermin steering inequality violation. From this bound, it follows that the violation of Mermin steering inequality by 3.5 certifies the GHZ-fidelity of 78.66% at least. On the other hand, the above maximal violation of Mermin steering inequality observed in our experimental setup is produced by a post-selected entangled state having the GHZ-fidelity of 87.25 ± 0.34% through quantum tomography.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Quantum correlation among multipartite systems is important not only for fundamental quantum physics but also for quantum information processing, such as quantum computation [1] and quantum communication [2]. It is now clear that quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering [3] and Bell nonlocality [4] forms a hierarchical structure of quantum nonlocality with the correlation strength increases. As the intermediate case, EPR steering in multipartite scenario is formalized as a quantum information task that Alice can convince others that she is able to steer their particles through her untrusted measurement device and corresponding outcomes. The steerability relies on that there exists no local hidden state model probably found by those know their own fully-characterized states and outcomes from Alice [3,5]. In addition, the intrinsic characteristic of asymmetry of EPR steering makes it an essential resource for semi-device-independent quantum information processing, which would be crucial to asymmetric quantum networks [6].

It was not until Bell inequality [7] derived from local hidden variable (LHV) theories that Bell nonlocality could be quantified experimentally. Following this breakthrough work, many efforts were made, such as performing tomography [8], constructing entanglement witness [9] and verifying the violation of various Bell-type inequalities [10–12]. Among these methods, observing the violation of Mermin inequality [13] is widely used in multipartite systems [14], for example, the tripartite Greenberger-Horne-Zeilinger (GHZ) state [15], etc. To be specific, we can certify genuine n-partite entanglement by observing the violation of Mermin inequality bound of 2n/2 for n even and 2(n−1)/2 for n odd. In addition, quantum mechanics allows an upper bound of Mermin inequality at 2n−1.

As a counterpart, several criteria have been derived to detect EPR steering [16]. For instance, the violation of steering inequalities based on moments matrix [17], all-versus-nothing proofs [18], Heisenberg uncertainty principle [19,20], entropy uncertainty principle [21,22], fine-grained uncertainty principle [23], and geometric Bell-like inequalities [24] leads to proof of existence of EPR steering. It has been demonstrated that the violation of tripartite Mermin inequality detects tripartite EPR steering in a two-sided device-independent way [25, 26] i.e., in the presence of two untrusted parties and the trusted party performing measurements in qubit mutually unbiased bases.

The genuine demonstration of EPR steering is still challenging even with the help of criteria above because of the detection loophole. Suffering from the low detection efficiency, all the events where at least one of the particles is not detected are rejected, which means the fair-sampling assumption is made in these cases. Take the Mermin steering inequality as an example, the minimum detection efficiency required for a loophole-free test is 75 % on each side of the tripartite system [27]. Unfortunately, the efficiencies of our single-photon detectors are around 63 % and the overall detector efficiency (defined as the ratio of detected to produced particles) of our setup is 18.2 % with 3 nm interference filter, which is far from closing the detect loophole. As a result, the violation of Mermin steering inequality in our experiment actually proves only the steerability of post-selected GHZ state, not the genuine demonstration of EPR steering.

In this paper, we present an experimental investigation of Mermin steering inequality on tripartite GHZ states. This article is organized as follows. Mermin steering inequality is theoretical derived in [25], and for completeness we introduce it briefly in Sec. II and discuss our motivations in this section. Tight lower bound on the GHZ-fidelity which can be certified by Mermin steering inequality is also derived in this section. We demonstrate the experimental setup in Sec. III, composed with two independent SPDC bipartite entangled sources. In Sec. IV, we describe the experimental process in detail and present analysis on the corresponding experimental results. Finally, we conclude with a summary and outlooks in Sec. V.

2. Motivation

Consider a tripartite scenario in which Alice, Bob and Charlie are three spatially separated parties. The three observers can perform some local measurements on their subsystems. In particular, each of the observer choose independently between two different dichotomic observables by using a single random bit (respectively denoted by x, y and z) taking values in 0 or 1. Thus the binary outcomes of each observer mark as a, band c taking values in +1 or −1. The conditional probability distribution P(abc|AxByCz) describes the probability of obtaining outcomes a, band c when the three observers perform measurements Ax, By and Cz, respectively. Hence, Mermin inequality [13] is in the form of

A0B0C1+A0B1C0+A1B0C0A1B1C1LHV2,
where AxByCz=abcabcP(abc|AxByCz). By measuring the probability of the outcomes, the Mermin inequality can be violated to its algebraic maximum of 4 by the GHZ state |ψGHZ=12(|000+|111).

Though the violation of Mermin inequality does not certify genuine nonlocality, it can be used to certify genuine entanglement in a fully device-independent way whenever its violation is more than 22 [28]. Furthermore, it has been shown that the maximal violation of Mermin inequality provides robust self-testing of the GHZ state [29], i.e., the maximal or near maximal violation of the Mermin inequality certifies the GHZ state up to local isometries. In [30], the author has provided an analytical tight lower bound on the GHZ-fidelity (fidelity of the state used for violating the Mermin inequality compared with the maximally entangled tripartite GHZ state) that can be certified by the Mermin inequality violation of more than 22. When the violation of the Mermin inequality more than 22 is observed by using a tripartite state ρABC in ℂd ⊗ ℂd ⊗ ℂd, our GHZ-fidelity is defined as follows:

FGHZ=maxΛA,ΛB,ΛCψGHZ|(ΛAΛBΛC)ρABC|ψGHZ,
where the maximum is taken over all the local extraction quantum channels, ΛA, ΛB and ΛC, (completely positive trace-preserving maps) of appropriate input and output registers. It has been demonstrated that for a given violation of Mermin inequality γ of more than 22, the GHZ-fidelity satisfies the following tight bound [30]
FGHZ12+12γ22422.
Thus, for the violation of Mermin inequality more than 22, one can certify a nontrivial GHZ-fidelity i.e., GHZ-fidelity of more than 50 % and the certified fidelity can be quantified by using the above lower bound.

Multipartite steering inequalities have been derived to witness multipartite entanglement in asymmetric networks in which some of the parties perform untrusted measurements while the other parties perform the trusted measurements [6, 25]. It has been demonstrated that the violation Mermin inequality can be used to witness tripartite steering in the context of a two-sided device-independent scenario. In this specific tripartite steering scenario, Alice and Bob claim that they can steer the state of the subsystem on Charlie’s side through performing uncharacterized local measurements on their respective subsystems. Hence there exists a LHV-LHS model when Alice and Bob fail to steer:

p(abc|AxByCz)=λpλPλ(a|Ax)Pλ(b|By)P(c|Cz,ρCλ),
for some hidden variable λ with probability distribution pλ, λpλ=1. P(c|Cz,ρCλ) are the distributions arising from local hidden states ρCλ. In this two-side-device-independent (2SDI) scenario where the untrusted parties’ Alice and Bob try to steer Charlie, there exists a steering inequality [25,26]
|A0B0C1+A0B1C0+A1B0C0A1B1C1?×?×2|LHVLHS2,
where ?×? × 2 indicates that Alice and Bob’s measurements are uncharacterized, while Charlie’s subsystem is assumed to be qubit and Charlie performs measurements in two mutually unbiased bases. If the quantum correlation violates Eq. (5), then it detects tripartite steering across the bipartite cut AB|C. Interestingly, the violation of Mermin steering inequality given by Eq. (5) by using a three-qubit state requires the presence of genuine tripartite entanglement [26]. Thus, the Mermin steering inequality can be used to witness tripartite steering in the simplest way.

In [31], robust two-sided device-independent self-testing of the GHZ state has been demonstrated theoretically by using the maximal violation of Mermin steering inequality. We now derive tight analytical self-testing bound, i.e., tight lower bound on the GHZ-fidelity that can be certified by the violation of Mermin steering inequality given by Eq. (5). In the context of our above two-sided device-independent scenario where Alice and Bob perform two black-box dichotomic measurements and Charlie performs measurements in two mutually unbiased bases of qubit dimension, our GHZ-fidelity is defined as follows:

FGHZ2SDI=maxλA,λBψGHZ|(λAλB𝟙)ρABC|ψGHZ,
where the maximum is taken over all the local extraction quantum channels acting only on the Alice and Bob’s sides and ρABC is a tripartite state in ℂd ⊗ ℂd ⊗ ℂ2 which is the state that gives rise to the observed violation of Mermin steering inequality. We now demonstrate that the above GHZ-fidelity satisfies the following tight lower bound [32].

Proposition 1 In the context of the violation of Mermin steering inequality, a nontrivial GHZ-fidelity is certifiable if and only if the violation γ>1/2 and the certifiable GHZ-fidelity can be quantified by the following tight bound

FGHZ2SDI12+12γ22422,
for the violation γ[22,4].

Proof 1 In [26], it has been demonstrated that there exists a family of tripartite correlations giving rising to the violation of Mermin steering inequality up to 22 which can be reproduced by a biseparable state in the context of our two-sided device-independent scenario. On the other hand, genuine tripartite entanglement is necessary for the violation of Mermin steering inequality beyond 22. Therefore, a nontrivial GHZ-fidelity is certifiable from the violation of Mermin steering inequality if and only if the violation γ>1/2.

Let us derive the bound on the GHZ-fidelity certifiable from the violation of Mermin steering inequality beyond 22. For this purpose, we note that the violation of Mermin steering inequality up to 22 can be achieved by the state |νABC = |Φ〉AB |0〉C (where |Φ〉AB is the singlet state up to local unitaries). This implies that the violation between 22 and 4 can be realized by a family of tripartite correlations which are a convex mixture of the two correlations arising from |νABC and |ϒABC=(|000+|111)/2 in the context of our two-sided device-independent scenario. In [30], it was shown that the above realization of violation of Mermin inequality between 22 and 4 implies the tight bound on the GHZ-fidelity given by Eq. (3) that can be certified in a fully device-independent way. From this, it follows that in the context of our two-sided device-independent scenario as well, this tight bound on the GHZ-fidelity holds.

3. Experimental setup

We implement an experimental demonstration of the Mermin steering inequality for a class of three-photon state shown in Fig. 1, i.e., the GHZ states

|GHZ=(|HAHBHCi|VAVBVC)/2,
where |H〉 and |V〉 represent horizontal and vertical polarizations, which are two directions of z axis in the Bloch sphere. The state source can be divided into three parts, two independent spontaneous parametric down-conversion (SPDC) sources. Firstly, generated by a mode-locked Ti:sapphire laser, a beam of light with a duration of less than 100 fs, a repetition rate of 80 MHz, and a central wavelength of 780 nm passes through a frequency doubler. Then, the ultraviolet pulsed light from the doubler pumps two SPDC sources in sequence.

 figure: Fig. 1

Fig. 1 Experimental setup for verifying the violation of Mermin steering inequality. It consists of two consecutive spontaneous parametric down-conversion (SPDC) sources. I-BBO: a β-barium borate (BBO) crystal cut for collinear type-I phase-matching; II-BBO: a BBO crystal cut for collinear type-II phase-matching; C-BBO: sandwich-type BBO+HWP+BBO combination; QWP: quarter-wave plate; HWP: half-wave plate; PBS: polarzing beam-splitter; IF2: interference filter with a full width at half maximum (FWHM) of 2 nm and central wavelength of 780 nm; IF3: interference filter with a FWHM of 3 nm and central wavelength of 780 nm; APD: single-photon detector.

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In the former SPDC source, two pieces of 1-mm beamlike-phase-matching type-II BBO crystals (BBO1 and BBO2), with one true-zero-order half-wave plate (THWP) inserted between them, form a sandwich-like structure [33]. These sandwich-like crystals are used for photon pair generation through the SPDC process. In this process, |He,1〉 denotes the extraordinary down-converted photons in the horizontal polarization from BBO1 and |Vo,2〉 denotes the ordinary down-converted photons in the vertical polarization from BBO2. The role of the inserted THWP is to rotate the down-converted photons |He,1〉 |Vo,1〉 from BBO1 to its orthogonal polarization |Ve,1〉 |Ho,1〉 while keeping the pump light polarization state nearly unchanged. Naturally, |Ve,1〉 (|Ho,1〉) and |He,2〉 (|Vo,2〉) remain spatial and temporal differences, which are compensated by a pair of LiNbO3 crystals and a pair of YVO4 crystals respectively. As a result, this pair of photons become indistinguishable with any information except polarization and is projected into the Bell state (1/2)(|HH+|VV). We perform quantum state tomography on the generated state and the fidelity is up to 98.45 ± 0.24 %. The only difference between the latter SPDC source and the former one is that the photons in mode D is projected in horizontal polarization, which heralds the photons in mode C′ with the same polarization.

To produce the maximally entangled GHZ state, photons in mode A′ are transmitted directly to the PBS, yet photons in mode C′ are rotated from |H〉 to |D〉 through the HWP1 formed an angle of 22.5° with its fast axis. They finally enter opposite ports of the PBS1 through two fibers. However, resulting mainly from the distance between two SPDC sources, photons pumped by the same pulse in mode A′ and C′ exist temporal difference. The PBS1 transmits horizontally-polarized component of photons in mode C′, and reflects vertically-polarized component of photons in mode A′. These photons emit through mode C without spatial difference. After the HWP before PBS2 rotated by 22.5°, HOM-like interference could be observed by APD1 and APD2 in mode C (triggering by APDs in mode Band D).

In other words, HOM-like interference with a visibility of 94.9 ± 2.2 % based on four-hold coincidences (observed by APD1, APD2 and APDs in mode Band D) ensures that it is almost impossible to distinguish two SPDC sources with any other information except polarization. With this indistinguishability, the source is projected into the GHZ state observed by APD1 and APDs in mode B, C and D. Finally, by rotating the angle of HWP1, the relative amplitudes of |HHH〉 and |VVV〉 can be tuned, and we get the GHZ-like state in form of

|GHZ=12(cos2θ|HAHBHCisin2θ|VAVBVC),
where θ is the angle of HWP1 forming with its fast axis. The density matrix of the maximally entangled GHZ state we prepared is shown in Fig. 2.

 figure: Fig. 2

Fig. 2 Quantum state tomography. Real (a) and imaginary (b) parts of the reconstructed density matrix of our GHZ state. The fidelity of our state compared with the ideal one is 87.25 ± 0.34 %.

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4. Experimental result

Specifically, when the measurements are preformed in the form of σx and σy, the Mermin steering inequality (5) with A0 = −σy, A1 = σx, B0 = −σy, B1 = σx, C0 = σx and C1 = σy can be rewritten as

|σyAσyBσyCσyAσxBσxCσxAσyBσxCσxAσxBσyCABC|2.
Here, ABC indicates that each expectation in the above sum of joint observables is measured when Charlie performs measurements on the conditional states prepared by Alice and Bob’s local measurements. To be specific, for σx and σy measurements, when we measure |D〉 or |L〉, the outcome is +1. When we measure |A〉 or |R〉, the outcome is −1. Here |D=(|H+|V)/2 and |A=(|H|V)/2, while |L=(|H+i|V)/2 and |R=(|Hi|V)/2. Coincidence counts for different measurements are listed in Table 1. Each item is the four-fold coincidence of mode A, B, C and D, with a duration of 300 seconds per measurement. The value of the inequality calculated by Eq. (6) for the GHZ state is 3.50 ± 0.05.

Tables Icon

Table 1. Four-fold Coincidence of the GHZ State under 32 Basis during 300 Seconds

The Mermin steering inequality can also be violated when some noise is introduced. State prepared in the form of Eq. (5) identifies with a mixture of the maximally entangled state and |HHH〉 works as noise. The parameters of Mermin steering inequality for states with different θ are measured and plotted in Fig. 3. We measured the parameter every other 5° when θ varied from 0° (|HHH 〉) to 22.5° (maximally entangled GHZ state). In Fig. 3, the experimental results fits the theoretical curve well. We can witness tripartite EPR steering around θ ∈ (9.2°, 22.5°).

 figure: Fig. 3

Fig. 3 Fig. 3 shows that different parameter of the Mermin steering inequality for states of Eq. (5) with different θ. θ represents the parameter of amplitudes of the state and can be varied with the rotation of the HWP1. The blue circles marked as ’Exp’ denote experimental data for Mermin parameters with error bars. The red curve marked as ’Theo’ represents theoretical predictions. EPR steering exists during θ ∈ (9.2°, 22.5°).

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5. Conclusion

We have experimentally prepared a tripartite GHZ entangled state and witnessed the violation of Mermin steering inequality. By carrying out quantum tomography on the generated states, we have reconstructed the density matrix and calculated the fidelity compared with maximally entangled GHZ state. As a result, we have achieved the state fidelity for GHZ state with 87.25 ± 0.34 %. Based on the reliable source, we measure the parameter of Mermin steering inequality with 3.50 ± 0.05. On the other hand, from the bound on the GHZ-fidelity given by Eq. (7) for the violation of Mermin steering inequality of γ = 3.5, it follows that the GHZ-fidelity of 78.66 % can be certified at least. Thus, our experimental setup has certified higher amount of GHZ-fidelity than the bound given by Eq. (3). In addition, we prepare a class of GHZ-like states and see a phase of Mermin parameters increasing with the growth of fidelity compared with the maximally entangled tripartite GHZ state. As soon as the Mermin steering inequality is observed, the GHZ-fidelity of the class of GHZ-like states exceeds 50 %. Thus, our experimental setup confirms tripartite steerability of post-selected entangled states by observing the violation of Mermin steering inequality.

In [6], the authors derived a tripartite steering inequality to detect tripartite steering of three-qubit states in the context of a two-sided device-independent scenario where each party performs three dichotomic measurements on their respective subsystems. The critical robustness to white noise of the GHZ state above which tripartite steering can be detected by using this inequality is 0.63. On the other hand, for the Mermin steering inequality, this bound reads 0.5. Thus, Mermin steering inequality provides a simpler way to detect tipartite EPR steering in the three-qubit states with higher GHZ-fidelity than the steering inequality presented in [6].

Funding

National Key R&D Program of China (2018YFA0306400, 2017YFA0304100); National Natural Science Foundation of China (61475197, 11774180, 61590932); Priority Academic Program Development of Jiangsu Higher Education Institutions; Postgraduate Research and Practice Innovation Program of Jiangsu Province. Ministry of Science and Technology of Taiwan (108-2811-M-006-501)

Acknowledgments

CJ thanks Manik Banik and Jedrzej Kaniewski for useful discussion and S. N. Bose Centre Kolkata for the postdoctoral fellowship.

References

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5. S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007). [CrossRef]  

6. D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015). [CrossRef]   [PubMed]  

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References

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  1. M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
    [Crossref]
  2. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
    [Crossref]
  3. H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
    [Crossref] [PubMed]
  4. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
    [Crossref]
  5. S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
    [Crossref]
  6. D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
    [Crossref] [PubMed]
  7. J. S. Bell, “On the einstein podolsky rosen paradox,” Physics 1, 195 (1964).
    [Crossref]
  8. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
    [Crossref]
  9. M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
    [Crossref] [PubMed]
  10. J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
    [Crossref]
  11. D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
    [Crossref] [PubMed]
  12. M. Seevinck and G. Svetlichny, “Bell-Type Inequalities for Partial Separability in n-Particle Systems and Quantum Mechanical Violations,” Phys. Rev. Lett. 89, 060401 (2002).
    [Crossref] [PubMed]
  13. N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states,” Phys. Rev. Lett. 65, 1838 (1990).
    [Crossref] [PubMed]
  14. J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nat. 403, 515 (2000).
    [Crossref]
  15. D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kaftos, ed. (Kluwer Academic, 1989).
    [Crossref]
  16. Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
    [Crossref]
  17. I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
    [Crossref] [PubMed]
  18. J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
    [Crossref] [PubMed]
  19. M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
    [Crossref]
  20. S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
    [Crossref]
  21. J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
    [Crossref]
  22. A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
    [Crossref]
  23. T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
    [Crossref]
  24. M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
    [Crossref]
  25. E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
    [Crossref]
  26. C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
    [Crossref]
  27. A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
    [Crossref] [PubMed]
  28. M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
    [Crossref]
  29. K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
    [Crossref]
  30. J. Kaniewski, “Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities,” Phys. Rev. Lett. 117, 070402 (2016).
    [Crossref] [PubMed]
  31. I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
    [Crossref]
  32. J. Kaniewski, Private communication.
  33. C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
    [Crossref]

2018 (2)

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

2016 (2)

J. Kaniewski, “Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities,” Phys. Rev. Lett. 117, 070402 (2016).
[Crossref] [PubMed]

I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
[Crossref]

2015 (5)

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

2014 (3)

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

2013 (4)

Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

2011 (1)

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

2009 (1)

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

2008 (1)

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

2007 (3)

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

2004 (1)

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

2002 (3)

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

M. Seevinck and G. Svetlichny, “Bell-Type Inequalities for Partial Separability in n-Particle Systems and Quantum Mechanical Violations,” Phys. Rev. Lett. 89, 060401 (2002).
[Crossref] [PubMed]

M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
[Crossref]

2001 (2)

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

M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
[Crossref]

2000 (1)

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nat. 403, 515 (2000).
[Crossref]

1990 (1)

N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states,” Phys. Rev. Lett. 65, 1838 (1990).
[Crossref] [PubMed]

1964 (1)

J. S. Bell, “On the einstein podolsky rosen paradox,” Physics 1, 195 (1964).
[Crossref]

Acín, A.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

Adesso, G.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

Aguilar, G.

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Andersen, U. L.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Armstrong, S.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Bachor, H.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Bachor, H. A.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Bancal, J. D.

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

Barrett, J.

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

Bell, J. S.

J. S. Bell, “On the einstein podolsky rosen paradox,” Physics 1, 195 (1964).
[Crossref]

Bhattacharya, B.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Bhattacharya, S. S.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Bourennane, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Bouwmeester, D.

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nat. 403, 515 (2000).
[Crossref]

Bowen, W.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Broadbent, C. J.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

Brunner, N.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

Bruß, D.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Cabello, A.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

Cavalcanti, D.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

Cavalcanti, E. G.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Chen, J. L.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Chuang, I.

M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
[Crossref]

Collins, D.

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Costa, A. C. S.

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

Daniell, M.

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nat. 403, 515 (2000).
[Crossref]

Das, D.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Doherty, A. C.

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

Drummond, P.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Dutta, A.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

Eibl, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Gaertner, S.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Gisin, N.

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Gong, Q.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kaftos, ed. (Kluwer Academic, 1989).
[Crossref]

Gühne, O.

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Guo, G. C.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

He, Q.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

He, Q. Y.

Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

Hoban, M. J.

I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
[Crossref]

Horne, M. A.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kaftos, ed. (Kluwer Academic, 1989).
[Crossref]

Howell, J. C.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

Huang, Y. F.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Hyllus, P.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

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, 052312 (2001).
[Crossref]

Janousek, J.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Jebaratnam, C.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Jones, S. J.

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

Kaniewski, J.

J. Kaniewski, “Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities,” Phys. Rev. Lett. 117, 070402 (2016).
[Crossref] [PubMed]

J. Kaniewski, Private communication.

Kaplan, M.

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

Kogias, I.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

Kurtsiefer, C.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Kwek, L. C.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Kwiat, P. G.

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

Lam, P. K.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Leuchs, G.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Lewenstein, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Li, C. F.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Liu, B. H.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Majumdar, A. S.

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

Mermin, N. D.

N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states,” Phys. Rev. Lett. 65, 1838 (1990).
[Crossref] [PubMed]

Mukherjee, A.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[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, 052312 (2001).
[Crossref]

Navascués, M.

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

Nery, R.

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Nielsen, M. A.

M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
[Crossref]

Oh, C. H.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Pál, K. F.

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

Pan, J. W.

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nat. 403, 515 (2000).
[Crossref]

Pironio, S.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

Popescu, S.

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Pramanik, T.

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

Reid, M.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Reid, M. D.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

Ribeiro, P. S.

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Riccardi, A.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Roberts, D.

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Rodriguez, D.

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

Roy, A.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Sanpera, A.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Sarkar, D.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Scarani, V.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Schneeloch, J.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

Seevinck, M.

M. Seevinck and G. Svetlichny, “Bell-Type Inequalities for Partial Separability in n-Particle Systems and Quantum Mechanical Violations,” Phys. Rev. Lett. 89, 060401 (2002).
[Crossref] [PubMed]

M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
[Crossref]

Skrzypczyk, P.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Su, H. Y.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Šupic, I.

I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
[Crossref]

Svetlichny, G.

M. Seevinck and G. Svetlichny, “Bell-Type Inequalities for Partial Separability in n-Particle Systems and Quantum Mechanical Violations,” Phys. Rev. Lett. 89, 060401 (2002).
[Crossref] [PubMed]

Teh, R. Y.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Thew, R.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

Uffink, J.

M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
[Crossref]

Uola, R.

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

Vértesi, T.

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

Villanueva, I.

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

Walborn, S.

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Walborn, S. P.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

Wang, M.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Wang, Z.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Wehner, S.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

Weinfurter, H.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nat. 403, 515 (2000).
[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, 052312 (2001).
[Crossref]

Wiseman, H. M.

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

Wu, C. F.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Ye, X. J.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Yin, Z.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

Zeilinger, A.

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nat. 403, 515 (2000).
[Crossref]

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kaftos, ed. (Kluwer Academic, 1989).
[Crossref]

Zhang, C.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Zukowski, M.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

Am. J. Phys. (1)

M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
[Crossref]

Entropy (1)

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

Nat. (1)

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nat. 403, 515 (2000).
[Crossref]

Nat. Commun. (1)

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

Nat. Phys. (1)

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

New J. Phys. (1)

I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
[Crossref]

Phys. Rev. A (10)

M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
[Crossref]

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

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

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

Phys. Rev. Lett. (10)

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

M. Seevinck and G. Svetlichny, “Bell-Type Inequalities for Partial Separability in n-Particle Systems and Quantum Mechanical Violations,” Phys. Rev. Lett. 89, 060401 (2002).
[Crossref] [PubMed]

N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states,” Phys. Rev. Lett. 65, 1838 (1990).
[Crossref] [PubMed]

Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

J. Kaniewski, “Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities,” Phys. Rev. Lett. 117, 070402 (2016).
[Crossref] [PubMed]

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Physics (1)

J. S. Bell, “On the einstein podolsky rosen paradox,” Physics 1, 195 (1964).
[Crossref]

Rev. Mod. Phys. (2)

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Sci. Rep. (1)

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Other (2)

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kaftos, ed. (Kluwer Academic, 1989).
[Crossref]

J. Kaniewski, Private communication.

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Figures (3)

Fig. 1
Fig. 1 Experimental setup for verifying the violation of Mermin steering inequality. It consists of two consecutive spontaneous parametric down-conversion (SPDC) sources. I-BBO: a β-barium borate (BBO) crystal cut for collinear type-I phase-matching; II-BBO: a BBO crystal cut for collinear type-II phase-matching; C-BBO: sandwich-type BBO+HWP+BBO combination; QWP: quarter-wave plate; HWP: half-wave plate; PBS: polarzing beam-splitter; IF2: interference filter with a full width at half maximum (FWHM) of 2 nm and central wavelength of 780 nm; IF3: interference filter with a FWHM of 3 nm and central wavelength of 780 nm; APD: single-photon detector.
Fig. 2
Fig. 2 Quantum state tomography. Real (a) and imaginary (b) parts of the reconstructed density matrix of our GHZ state. The fidelity of our state compared with the ideal one is 87.25 ± 0.34 %.
Fig. 3
Fig. 3 Fig. 3 shows that different parameter of the Mermin steering inequality for states of Eq. (5) with different θ. θ represents the parameter of amplitudes of the state and can be varied with the rotation of the HWP1. The blue circles marked as ’Exp’ denote experimental data for Mermin parameters with error bars. The red curve marked as ’Theo’ represents theoretical predictions. EPR steering exists during θ ∈ (9.2°, 22.5°).

Tables (1)

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Table 1 Four-fold Coincidence of the GHZ State under 32 Basis during 300 Seconds

Equations (10)

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A 0 B 0 C 1 + A 0 B 1 C 0 + A 1 B 0 C 0 A 1 B 1 C 1 LHV 2 ,
F GHZ = max Λ A , Λ B , Λ C ψ GHZ | ( Λ A Λ B Λ C ) ρ ABC | ψ GHZ ,
F GHZ 1 2 + 1 2 γ 2 2 4 2 2 .
p ( a b c | A x B y C z ) = λ p λ P λ ( a | A x ) P λ ( b | B y ) P ( c | C z , ρ C λ ) ,
| A 0 B 0 C 1 + A 0 B 1 C 0 + A 1 B 0 C 0 A 1 B 1 C 1 ? × ? × 2 | LHV LHS 2 ,
F GHZ 2 SDI = max λ A , λ B ψ GHZ | ( λ A λ B 𝟙 ) ρ ABC | ψ GHZ ,
F GHZ 2 SDI 1 2 + 1 2 γ 2 2 4 2 2 ,
| GHZ = ( | H A H B H C i | V A V B V C ) / 2 ,
| GHZ = 1 2 ( cos 2 θ | H A H B H C i sin 2 θ | V A V B V C ) ,
| σ y A σ y B σ y C σ y A σ x B σ x C σ x A σ y B σ x C σ x A σ x B σ y C A B C | 2 .

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