Abstract

Based on the circuit including linear optical elements, a fault-tolerant distribution of GHZ states against collective noise among three parties is proposed. Additionally, two controlled DSQC protocols using the shared GHZ states as quantum channels are also presented under the charge of the controller. The first controlled DSQC protocol applies single parity analysis based on weak cross-Kerr nonlinearities. The receiver Bob performs single-photon measurement to obtain the secret information after the outcome publication of the single parity analysis executed by the sender Alice. The second protocol applies dense coding to double information transmission capacity, and the double parity analyses based on weak cross-Kerr nonlinearities are performed to obtain the secret information.

© 2017 Optical Society of America

1. Introduction

Combining the techniques of classical cryptography and quantum mechanics, quantum cryptography [1] is one of the most striking and charming developments in the communication field. Employing the principle of quantum mechanics, the legitimate participants can communicate with each other in a private and secret way.

Referring to classical key distribution, quantum key distribution (QKD) was proposed and has made a great progress. Due to the different generation modes of the secret key, there are two kinds of quantum key distribution. One is the random quantum key distribution, such as the protocols of the individual information carriers (BB84-QKD protocol [2] and B92-QKD protocol [3]) and the protocols using quantum entanglement (E91-QKD protocol [4] and BBM92-QKD protocol [5]). The other is deterministic quantum key distribution, for instance, the protocol using order rearrangement of the photons [6].

Long and Liu proposed another kind of quantum communication methods [7], quantum secure deterministic communication (QSDC), which is actually the direct quantum communication without using the key, and the secret information are sent directly through the quantum channel. Following this idea, Deng et al. presented two QSDC protocols using the methods of two-step [8] and one-time pad [9] respectively. Recently, the entanglement based QSDC protocols [7] and the two-step QSDC protocol [8] have been experimentally demonstrated [10]. And the one-time pad QSDC protocol [9] is experimentally realized [11] in a noisy and lossy environment.

Deterministic secure quantum communication (DSQC) can send information deterministically and be read out by the receiver after receiving another classical communication from the sender. DSQC is actually a variant of deterministic QKD. Normally, one first establishes the key, and then encrypts the information into ciphertext, and sends the ciphertext through a classical communication. In DSQC, one can send the ciphertext through the quantum channel first, and if the transmission is secure, then the key can be sent through a classical channel to the receiver. Essentially, DSQC is a combined process of deterministic QKD plus a classical communication [12–16].

In some scenarios, information transmission and communication between two legitimate participants should be in the charge of a controller. In different physical environment, a large amount of controlled deterministic secure quantum communication (Controlled DSQC) protocols were proposed [17–20]. As to the realization of Controlled DSQC, entanglement is a useful resource. Recently, there are many researches about the entanglement generation [21–25], the entanglement concentration [26], the entanglement distribution [26] and transmission [21], and the applications of entanglement [27], such as teleportation [28], quantum state sharing [29], quantum operation sharing [30], and hyperentanglement applications [27].

Noise does great harm to communication. It reduces the accuracy and security of the communication protocols. There are many useful methods to alleviate the noise effect, such as error correction [31], entanglement concentration [32–34], and self-stabilizing algorithm [35]. In practice, if we select photons as information carriers and the free space or the optical fiber as the transmitting paths of photons, the collective noise channel will be a reasonable assumption, which means that the transmitted photons are sufficient near to each other in the space or time interval so that the noise can not judge their difference and the photons suffer from the same noise.

Based on this reasonable assumption and the corresponding elaborate processing and operations, some communication protocols can be realized [36–39].

Taking the collective noise into account, we propose two controlled DSQC protocols exploiting GHZ states in the optical systems. At first, the secure distribution is presented to tolerantly distribute two photons of three-photon GHZ states from the controller to two legitimate participants via collective noise channels. Based on weak cross-Kerr nonlinearities, two explicit controlled DSQC protocols with GHZ states employing single parity analysis and double parity analyses are proposed.

2. Controlled DSQC protocols based on fault-tolerant distribution of GHZ states

It needs to note that the realization of two controlled DSQC protocols are based on the secure distribution of GHZ states. Based on the secure distribution of GHZ states, Hillery et al. [29] presented the first secret sharing protocol, which is considered in the ideal environment. Here we consider the secure distribution of the quantum channel comprised of GHZ states against collective noise.

2.1. The secure distribution of GHZ states as the quantum channel

Suppose that the controller Charlie possesses GHZ states expressed as

|GHZAiBiCi=12(|HHH+|VVV)AiBiCi,
where |H〉 and |V〉 denote the horizontal polarization mode and vertical polarization mode of the photons.

Illustrated in Fig. 1, Charlie distributes photon Ai and photon Bi from each GHZ polarization-entangled state to two communicators Alice and Bob through path PA (channel CA1 and channel CA2) and path PB (channel CB1 and channel CB2) respectively.

 figure: Fig. 1

Fig. 1 An illustration plot for distributing photon Ai and photon Bi of a GHZ state from Charlie to Alice (path A) and Bob (path B) via the collective noise channel. The components PBSA1, PBSA2, PBSB1, and PBSB2 reflect the state |V〉 and transmit the state |H〉. A half wave plate (HWP 45°) where the angle of 45° between the optical axis and horizontal polarization mode |H〉 is set, is inserted into the line, which functions as a NOT gate to realize the state exchange of |H〉 and |V〉.

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Here, we consider the collective noise channel. Under the assumption of collective noise, the photon Ai sent to Alice via the channel CA1 and the channel CA2 suffers from the identical noise, and the photon Bi sent to Bob via the channel CB1 and the channel CB2 suffers from the identical noise respectively.

For the requirement of communication security and lesser communication cost, communication sequence is transmitted by photon blocks [7, 8]. If one photon block encounters trouble, it will be discarded. However, its failure can not affect other blocks. Furthermore, before sending A-sequence (is composed of photons Ai) and B-sequence (is composed of photons Bi), Charlie changes the order of the transmitted photons [6,14,15], which can also be used to prevent from the Toffoli gate attack [40–42] and guarantee his controlled function.

After the photon Ai and the photon Bi pass through polarization beam splitters, PBSA1 and PBSB1, the GHZ state to be distributed can be denoted as

12(|HHAiBi|CA2CB2|HCi+|VVAiBi|CA1CB1|VCi),
where |CA1CB1〉 and |CA2CB2〉 stand for the spatial modes of the photons (Ai, Bi), which are corresponding to their polarization modes |HHAi,Bi and |VVAi,Bi.

To articulate the fault-tolerant distribution, here we adopt the representation of the product state of the polarization modes and the spatial modes of the photons (Ai, Bi). As for the photon Ci, we express their states by only using the polarization modes, that is, |HCi and |VCi.

Half wave plates HWP45A11° and HWP45B11° functioning as a NOT gate change the state denoted as Eq. (2) to

12|HHAiBi(|HCi|CA2CB2+|VCi|CA1CB1).

Before entering into the collective noise channel, the initial state of the whole system is

ρ=ρ1ρ2,ρ1=|HHAiBiHH|,ρ2=12(|HCi|CA2CB2+|VCi|CA1CB1)(H|CiCA2CB2|+V|CiCA1CB1|).

Suffered from the collective noise, the polarization mode of the transmitted photons Ai, Bi evolves as

ρ1=|HHAiBiHH|ρ1=k,l,m,n=12αklmn|klAiBimn|,
where the coefficients αklmn (k, l, m, n = 1 or 2) denote the noise parameters which are only corresponding to the different paths (PA, PB), rather than the different channels ({CA1, CA2}, {CB1, CB2}) in the same path, and we adopt the symbols |1〉 ≡ |H〉, |2〉 ≡ |V〉 for simplification.

Leaving from the collective noise channels, the photon Ai and the photon Bi are allowed to pass through HWP45x12°, and their state evolves as

ρ1ρ212(|VCiV||CA1CB1CA1CB1|k,l,m,n=12αklmn|k¯,l¯AiBim¯n¯|+|VCiH||CA1CB1CA2CB2|k,l,m,n=12αklmn|k¯,l¯AiBim¯n¯|+|HCiV||CA2CB2CA1CB1|k,l,m,n=12αklmn|k,lAiBim¯n¯||HCiH||CA2CB2CA2CB2|k,l,m,n=12αklmn|k,lAiBimn|),
where, |1̄〉 ≡ |2〉, |2̄〉 ≡ |1〉.

Subsequently, the photon Ai and the photon Bi go through PBSx2,

12k,l,m,n=12[αklmn|CAkCBlCAmCBn||VCiV||k¯,l¯AiBim¯n¯|+|VCiH||k¯,l¯AiBim¯n¯|+|HCiV||k,lAiBim¯n¯|+|HCiH||k,lAiBimn|].

And then, the photon Ai and the photon Bi get through HWP45x2° (x = A, B), and the state can be denoted as

12k,l,m,n=12αklmn|CAkCBlCAmCBn|(|HHH+|VVV)AiBiCi(HHH|+VVV|).

Finally, Alice and Bob obtain the photon Ai and the photon Bi at the output ports (OA1, OB1), ports (OA1, OB2), ports (OA2, OB1), or ports (OA2, OB2) with probabilities α1111, α1212, α2121, or α2222 respectively. That is to say, the photon Ai and the photon Bi in GHZ states can be distributed deterministically from Charlie to Alice and Bob via the collective noise channels.

After photon blocks are distributed, Alice and Bob perform the measurement along two nonorthogonal sets of orthogonal bases {|H〉, |V〉} and {|+=12(|H+|V), |=12(|H|V)} at random to check security of the distribution procedure, by which the legitimate participants can confirm the fact whether there is an eavesdropper on the line or not. Taking the imperfect factors into account, Alice and Bob evaluate the disadvantageous influence and set the threshold value of communication security. That is, the error rate beyonds the value will be reviewed as a dangerous signal and the legitimate participants discard this block and check other blocks.

Confirming no eavesdropping, the communication between Alice and Bob can be processed by employing the other photons of this photon block under Charlie’s agreement and cooperation.

Here, we consider two controlled DSQC protocols on the basis of the above preparatory work.

Cooperating with Alice and Bob, Charlie needs to perform single-photon measurements under the basis of {|+〉, |−〉} on the communication photon group Cc, and publicizes the measurement outcomes and the corresponding correct order of communication photons. The publicized information and the measurement outcomes are subject to the rule that ‘0’ corresponds to |+〉 and ‘1’ corresponds to |−〉.

2.2. The first controlled DSQC protocol with single parity analysis

At first, we propose the first controlled DSQC protocol with local nondemoliton single parity analysis. Local single parity analysis is exploited to distinguish parity states, while the discrimination of Bell states is not necessary. Moreover, the resulted states after nondemoliton parity analyses can be continued to fulfil other tasks of quantum information processing.

Alice possesses the encoding photons (photons Ei), called as E-sequence, which are encoded based on the rules: a photon in the state |+〉 is corresponding to secret information ‘0’ and a photon in the state |−〉 corresponds to secret information ‘1’. Alice wants to send the secret information to Bob.

After two communicators obtain Charlie’s permission, Alice performs single parity analysis on the photon Ei and the photon Ai along the basis of {|+〉, |−〉}. Based on weak cross-Kerr nonlinearities, the parity analysis can be realized nearly deterministically [43–49], illustrated in Fig. 2, and as a consequence Alice achieves the parity states which can be denoted as

|Even+=12(|++±|),|Odd+=12(|+±|+).

After that, Alice publicizes the measurement outcomes. Explicitly, if her measurement outcome is |Even+−, Alice sends the information ‘0’ to Bob, and if her measurement outcome is |Odd+−, Alice sends the information ‘1’ to Bob.

 figure: Fig. 2

Fig. 2 A schematic plot of parity analysis. PBSHV (±)1 and PBSHV (±)2 represent the polarization beam splitter transmitting |H〉 (|+〉) mode and reflecting |V〉 (|−〉) mode. θ and 2θ denote phase shifts occurred on the coherent state |α〉. After the phase modulation −3θ, the measurement on the affected coherent state is performed. According to the measurement outcomes, a phase modulation 2ϕ is performed to eliminate the phase difference of one scenario (photons (1,2) pass through path 1′) and another scenario (photons (1,2) pass through path 2′), if the measurement witnesses the existence of nonzero phase shift.

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After he receives the parity analysis information from Alice, Bob performs single-photon measurement along the basis of {|+〉, |−〉}, and registers the measurement outcomes according to the following rules. If his single-photon measurement outcome is |+〉, he records ‘0’, while if his measurement outcome is |−〉, he records ‘1’.

Finally, on the basis of the above information, Bob can obtain the secret information sent from Alice according to the addition rule of binary systems, that is, secret information=Charlie’s measurement outcome ⊕ Alice’s parity analysis information ⊕ Bob’s measurement outcome, which can be referred to Table 1.

Tables Icon

Table 1. The relations among the outcomes of measurement performed by three participants and the secret information: Charlie’s measurement outcomes ({|+〉, |−〉}) on the control photons Cc and the corresponding publicized information (C. M. Os.), Alice’s parity analysis outcomes and the corresponding publicized information (A. P. A. Os.), Bob’s single-photon measurement outcomes (B. S. P. M. Os.), and the obtained secret information (S. I.).

2.3. The second controlled DSQC protocol with double parity analyses and dense coding

Next, we describe the second controlled DSQC protocol with local double nondemoliton parity analyses and dense coding.

Firstly, Alice performs single-photon unitary transformations I, X, Y, and Z denoted as

I=|++|+||,X=|+|+|+|,Y=|+||+|,Z=|++|||,
to encode secret information on her photons, on the basis of the encoding rule: 00 : I, 01 : Z, 10 : X, and 11 : Y.

Subsequently, Alice sends the encoding photons to Bob by fault-tolerant distribution, which is similar to the transmitting process of the photon Ai from Charlie to her.

After reception of the photons sent from Alice, Bob performs the first parity analysis on photons (Ac, Bc) to check security. If the security check is passed, Bob can obtain the secret information by performing the second parity analysis to distinguish Bell states. That is called as double parity analyses which mean that two continuous parity analyses are performed along two different measurement bases. The double parity analyses can also be realized with the circuit illustrated in Fig. 2. Explicitly, if the first parity analysis is performed under the basis of {|H〉, |V〉}({|+ 〉, |−〉}), the second parity analysis should be performed on the basis of {|+〉, |−〉}({|H〉, |V〉}).

The detailed relations among Charlie’s single-photon measurement outcomes, Alice’s encoding operations, the resulted states, the outcomes of double nondemolition parity analyses, and the secret information sent from Alice can be found in Table 2, where Bell states along the basis of {|+〉, |−〉} can be denoted as

|Φ++=12(|+++|),|Φ+=12(|++|),|Ψ++=12(|++|+),|Ψ+=12(|+|+),
and
|EvenHV=12(|HH±|VV),|OddHV=12(|HV±|VH).

Tables Icon

Table 2. The relations among Charlie’s single-photon measurement outcomes (C. S.P.M.Os.), Alice’s encoding operations (A. E.Os.), the resulted states (R.Ss.), Bob’s double parity analysis outcomes (B. D.P.A.Os.), and the secret information (S.I.) sent from Alice.

The photons carried secret information are transmitted from Alice to Bob, so Trojan horse attacks need to be considered. To counterattack Trojan horse attacks, the corresponding countermeasures should be adopted, that is, a wavelength filter before Alice’s reception device to hold back the entry of the photons with the illegitimate frequencies, accurately controlling the operation time of reception window to prevent from delay-time photons, and counting the photon number or putting a photon number splitter to check the trace of multi-photon signals [1,50,51].

3. Error rate and efficiency

In the above two protocols, the measurement error occurs due to imperfect measurement methods, that is, the odd parity and even parity can not be fully distinguished if X Homodyne measurement [43, 52, 53] is applied. When displacement measurement [54–56] or photon number measurement based on double cross-Kerr nonlinearities [45, 46] is applied, the error rates are lowered largely but they need more complicated operations. Here, taking X Homodyne measurement as an example, the error rate of the first Controlled DSQC protocol can be denoted as [43,53]

Perr1=12erfc[α(1cosθ)/2],
and the error rate of the second Controlled DSQC protocol is
Perr2=erfc[α(1cosθ)/2].

Taking the effect of photon losses into accounted, a model of a beam splitter [57–59] is exploited, where the photon dissipation changes the amplitude α of the coherent state to the ηr α(0 ≤ ηr ≤ 1). So the error rate is increased to Perr1=12erfc[ηrηdα(1cosθ)/2] and Perr2=erfc[ηrηdα(1cosθ)/2], where ηd denotes the efficiency of detectors.

Illustrated in Fig. 3, if the sufficient large phase shift and large amplitude of the coherent state are available, two protocols can be realized with nearly deterministic probabilities. Moreover, due to double parity analyses, the error rate of the second Controlled DSQC protocol is higher than that of the first Controlled DSQC protocol.

 figure: Fig. 3

Fig. 3 The error rates of two protocols. The dimensionless parameters are set as: the practicable phase shift is 20° [60] and the efficiency of detectors is ηd = 91% [61]. The error rate of the first protocol and the error rate of the second protocol are plotted in the red dotted line and the blue solid line respectively, which vary with the amplitude of the coherent state.

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As for the efficiencies of two protocols, the classical transmission information needs to be considered [62–64]. In the first Controlled DSQC protocol, one-bit secret information can be obtained per two-bit classical information (one-bit is Charlie’s classical information and one-bit is Alice’s parity analysis outcome). In the second Controlled DSQC protocol, two-bit secret information can be obtained per one-bit classical information (Charlie’s classical information). Furthermore, the obtained states after nondemolition double parity analyses are not destroyed and can be repeatedly exploited in other protocols, and consequently the communication cost is reduced.

4. Conclusion

Based on the fault-tolerant distribution of GHZ states via the collective noise channels, we propose two controlled DSQC protocols to realize that two participants transmit secret information under the control of the controller. The security of communication and the controlled function of the controller can be confirmed by the security check and the order rearrangement of transmitted photons. The data block transmission reduces effectively communication cost.

In the first protocol, two participates apply two nonorthogonal sets of orthogonal bases measurements to check the security. Then Alice performs the single parity measurement to encode the secret information, and Bob performs the single-photon measurement to decode the secret information. So the first protocol is simple and easy to operate.

In the second protocol, employing dense coding, the information capacity is doubled. Nondemolition double parity analyses are applied, and as a consequence the obtained states can be repeatedly exploited in other protocols after measurement, so the cost is reduced in the second protocol.

Based on cross-Kerr nonlinearities, some tasks of quantum information processing have been proposed [49,65–74], so two controlled DSQC protocols presented here are expectable.

Funding

National Natural Science Foundation of China (NSFC) (11674037, 11544013, 11305016, 61301133, 11271055) and Natural Science Foundation of Liaoning Province (20170540010).

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49. X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Two-party quantum privacy comparison with polarization-entangled Bell states and the coherent states,” Quantum Inf. Comput. 14, 0236–0254 (2014).

50. F.-G. Deng, X.-H. Li, H.-Y. Zhou, and Z.-j. Zhang, “Improving the security of multiparty quantum secret sharing against Trojan horse attack,” Phys. Rev. A 72, 044302 (2005). [CrossRef]  

51. Q.-Y. Cai, “Eavesdropping on the two-way quantum communication protocols with invisible photons,” Phys. Lett. A 351, 23–25 (2006). [CrossRef]  

52. M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University, Cambridge, 1997). [CrossRef]  

53. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical Controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004). [CrossRef]  

54. W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005). [CrossRef]  

55. S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006). [CrossRef]  

56. H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006). [CrossRef]  

57. U. Leonhardt, “Quantum statistics of a lossless beam splitter: SU(2) symmetry in phase space,” Phys. Rev. A 48, 3265–3277 (1993). [CrossRef]   [PubMed]  

58. G. M. D’Ariano, “A group-theoretical approach to the quantum damped oscillator,” Phys. Lett. A 187, 231–235 (1994). [CrossRef]  

59. M. Bartkowiak, L.-A. Wu, and A. Miranowicz, “Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing,” J. Phys. B 47, 145501 (2014). [CrossRef]  

60. I.-C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial Atom,” Phys. Rev. Lett. 111, 053601 (2013). [CrossRef]   [PubMed]  

61. W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, “High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits,” Nat. commun. 3, 1325 (2012). [CrossRef]   [PubMed]  

62. H.-Y. Dai, P.-X. Chen, and C.-Z. Li, “Probabilistic teleportation of an arbitrary two-particle state by a partially entangled three-particle GHZ state and W state,” Opt. Commun. 231, 281–287 (2004). [CrossRef]  

63. H.-Y. Dai, P.-X. Chen, L.-M. Liang, and C.-Z. Li, “Classical communication cost and remote preparation of the four-particle GHZ class state,” Phys. Lett. A 355, 285–288 (2006). [CrossRef]  

64. H.-Y. Dai, M. Zhang, and L.-M. Kuang, “Classical Communication Cost and Remote Preparation of Multi-qubit with Three-Party,” Commun. Theor. Phys. 50, 73–76 (2008). [CrossRef]  

65. G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989). [CrossRef]   [PubMed]  

66. Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010). [CrossRef]  

67. X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger-Horne-Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013). [CrossRef]  

68. L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014). [CrossRef]  

69. Y.-B. Sheng and F.-G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010). [CrossRef]  

70. X.-H. Li and S. Ghose, “Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity,” Opt. Express 23, 3550–3562 (2015). [CrossRef]   [PubMed]  

71. L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016). [CrossRef]  

72. W.-X. Cui, S. Hu, H.-F. Wang, A.-D. Zhu, and S. Zhang, “Deterministic conversion of a four-photon GHZ state to a W state via homodyne measurement,” Opt. Express 24, 15319 (2016). [CrossRef]   [PubMed]  

73. X.-M. Xiu, Q.-Y. Li, Y.-F. Lin, H.-K. Dong, L. Dong, and Y.-J. Gao, “Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities,” Phys. Rev. A 94, 042321 (2016). [CrossRef]  

74. L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016). [CrossRef]   [PubMed]  

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  56. H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
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  66. Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
    [Crossref]
  67. X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger-Horne-Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
    [Crossref]
  68. L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014).
    [Crossref]
  69. Y.-B. Sheng and F.-G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
    [Crossref]
  70. X.-H. Li and S. Ghose, “Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity,” Opt. Express 23, 3550–3562 (2015).
    [Crossref] [PubMed]
  71. L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
    [Crossref]
  72. W.-X. Cui, S. Hu, H.-F. Wang, A.-D. Zhu, and S. Zhang, “Deterministic conversion of a four-photon GHZ state to a W state via homodyne measurement,” Opt. Express 24, 15319 (2016).
    [Crossref] [PubMed]
  73. X.-M. Xiu, Q.-Y. Li, Y.-F. Lin, H.-K. Dong, L. Dong, and Y.-J. Gao, “Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities,” Phys. Rev. A 94, 042321 (2016).
    [Crossref]
  74. L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016).
    [Crossref] [PubMed]

2017 (3)

W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum Secure Direct Communication with Quantum Memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

F.-G. Deng, B.-C. Ren, and X.-H. Li, “Quantum hyperentanglement and its applications in quantum information processing,” Sci. Bull. 62, 46–68 (2017).
[Crossref]

B. K. Park, M. S. Lee, M. K. Woo, Y.-S. Kim, S.-W. Han, and S. Moon, “QKD system with fast active optical path length compensation,” Sci. China Phys. Mech. 60, 060311 (2017).
[Crossref]

2016 (7)

T. Li and Z. Q. Yin, “Quantum superposition, entanglement, and state teleportation of a microorganism on an electromechanical oscillator,” Sci. Bull. 61, 163–171 (2016).
[Crossref]

K. J. Zhang, L. Zhang, T. T. Song, and Y. H. Yang, “A potential application in quantum networks-Deterministic quantum operation sharing schemes with Bell states,” Sci. China Phys. Mech. 59, 660302 (2016).
[Crossref]

J.-Y. Hu, B. Yu, M.-Y. Jing, L.-T. Xiao, S.-T. Jia, G.-Q. Qin, and G.-L. Long, “Experimental quantum secure direct communication with single photons,” Light Sci. Appl. 5, e16144 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

W.-X. Cui, S. Hu, H.-F. Wang, A.-D. Zhu, and S. Zhang, “Deterministic conversion of a four-photon GHZ state to a W state via homodyne measurement,” Opt. Express 24, 15319 (2016).
[Crossref] [PubMed]

X.-M. Xiu, Q.-Y. Li, Y.-F. Lin, H.-K. Dong, L. Dong, and Y.-J. Gao, “Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities,” Phys. Rev. A 94, 042321 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016).
[Crossref] [PubMed]

2015 (7)

X.-H. Li and S. Ghose, “Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity,” Opt. Express 23, 3550–3562 (2015).
[Crossref] [PubMed]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-P. Ren, and Y.-J. Gao, “Quantum secure direct communication against the collective noise with polarization-entangled Bell states,” Prog. Theor. Exp. Phys. 2015, 123A02 (2015).
[Crossref]

R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96–100 (2015).
[Crossref]

H. Yan and J. F. Chen, “Narrowband polarization entangled paired photons with controllable temporal length,” Sci. China Phys. Mech. 58, 074201 (2015).
[Crossref]

C. Wang, W.-W. Shen, S.-C. Mi, Y. Zhang, and T.-J. Wang, “Concentration and distribution of entanglement based on valley qubits system in graphene,” Sci. Bull. 60, 2016–2021 (2015).
[Crossref]

C.-C. Qu, L. Zhou, and Y.-B. Sheng, “Entanglement concentration for concatenated Greenberger-Horne-Zeilinger state,” Quantum Inf. Process. 14, 4131–4146 (2015).
[Crossref]

Y. Sheng, J. Pan, R. Guo, L. Zhou, and L. Wang, “Efficient N-particle W state concentration with different parity check gates,” Sci. China Phys. Mech. 58, 060301 (2015).
[Crossref]

2014 (3)

L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014).
[Crossref]

M. Bartkowiak, L.-A. Wu, and A. Miranowicz, “Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing,” J. Phys. B 47, 145501 (2014).
[Crossref]

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Two-party quantum privacy comparison with polarization-entangled Bell states and the coherent states,” Quantum Inf. Comput. 14, 0236–0254 (2014).

2013 (4)

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules,” Prog. Theor. Exp. Phys. 2013, 093A01 (2013).
[Crossref]

I.-C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial Atom,” Phys. Rev. Lett. 111, 053601 (2013).
[Crossref] [PubMed]

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger-Horne-Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[Crossref]

H.-F. Wang, A.-D. Zhu, and S. Zhang, “Physical optimization of quantum error correction circuits with spatially separated quantum dot spins,” Opt. Express 21, 12484–12494 (2013).
[Crossref] [PubMed]

2012 (2)

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, “High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits,” Nat. commun. 3, 1325 (2012).
[Crossref] [PubMed]

2011 (3)

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

L. Dong, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel,” J. Exp. Theor. Phys. 113, 583–591 (2011).
[Crossref]

H.-F. Wang, S. Zhang, A.-D. Zhu, X. X. Yi, and K.-H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
[Crossref]

2010 (4)

S.-J. Qin, F. Gao, F.-Z. Guo, and Q.-Y. Wen, “Comment on ‘Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair’,” Phys. Rev. A 82, 36301 (2010).
[Crossref]

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
[Crossref]

Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

Y.-B. Sheng and F.-G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

2009 (2)

B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[Crossref]

H.-F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009).
[Crossref]

2008 (2)

Y.-F. Xiao, S. K. Özdemir, V. Gaddam, C.-H. Dong, N. Imoto, and L. Yang, “Quantum nondemolition measurement of photon number via optical Kerr effect in an ultra-high-Q microtoroid cavity,” Opt. Express 16, 21462 (2008).
[Crossref] [PubMed]

H.-Y. Dai, M. Zhang, and L.-M. Kuang, “Classical Communication Cost and Remote Preparation of Multi-qubit with Three-Party,” Commun. Theor. Phys. 50, 73–76 (2008).
[Crossref]

2007 (4)

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[Crossref]

F. Gao, Q.-Y. Wen, and F.-C. Zhu, “Comment on: ‘Quantum exam’ [Phys. Lett. A 350 (2006) 174],” Phys. Lett. A 360, 748–750 (2007).
[Crossref]

Y. Xia and H.-S. Song, “Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding,” Phys. Lett. A 364, 117–122 (2007).
[Crossref]

G.-l. Long, F.-g. Deng, C. Wang, X.-h. Li, K. Wen, and W.-y. Wang, “Quantum secure direct communication and deterministic secure quantum communication,” Front. Phys. China 2, 251–272 (2007).
[Crossref]

2006 (9)

H.-F. Wang and S. Zhang, “Quantum Secure Direct Communication by Using a GHZ State,” J. Korean Phys. Soc. 49, 459–463 (2006).

A.-D. Zhu, Y. Xia, Q.-B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A 74, 054302 (2006).
[Crossref]

J. Wang, Q. Zhang, and C.-j. Tang, “Multiparty controlled quantum secure direct communication using Greenberger-Horne-Zeilinger state,” Opt. Commun. 266, 732–737 (2006).
[Crossref]

C.-B. Fu, Y. Xia, B.-X. Liu, S. Zhang, K.-H. Yeon, and C.-I. Um, “Controlled Quantum Dense Coding in a Four-particle Non-maximally Entangled State via Local Measurements,” J. Korean Phys. Soc. 46, 1080–1082 (2006).

H.-Y. Dai, P.-X. Chen, L.-M. Liang, and C.-Z. Li, “Classical communication cost and remote preparation of the four-particle GHZ class state,” Phys. Lett. A 355, 285–288 (2006).
[Crossref]

Q.-Y. Cai, “Eavesdropping on the two-way quantum communication protocols with invisible photons,” Phys. Lett. A 351, 23–25 (2006).
[Crossref]

S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
[Crossref]

H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[Crossref]

2005 (7)

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[Crossref]

F.-G. Deng, X.-H. Li, H.-Y. Zhou, and Z.-j. Zhang, “Improving the security of multiparty quantum secret sharing against Trojan horse attack,” Phys. Rev. A 72, 044302 (2005).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
[Crossref]

Y. Xia, C.-B. Fu, F.-Y. Li, and S. Zhang, “Controlled Secure Direct Communication by Using GHZ Entangled State,” J. Korean Phys. Soc. 47, 753–756 (2005).

Y. Zhang, W.-C. Cao, and G.-L. Long, “Creation of Multipartite Entanglement and Entanglement Transfer via Heisenberg Interaction,” Chinese Phys. Lett. 22, 2143–2146 (2005).
[Crossref]

T. Yamamoto, J. Shimamura, S. K. Özdemir, M. Koashi, and N. Imoto, “Faithful Qubit Distribution Assisted by One Additional Qubit against Collective Noise,” Phys. Rev. Lett. 95, 040503 (2005).
[Crossref] [PubMed]

X.-B. Wang, “Fault tolerant quantum key distribution protocol with collective random unitary noise,” Phys. Rev. A 72, 050304(R) (2005).
[Crossref]

2004 (4)

J.-C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. Spekkens, “Robust Polarization-Based Quantum Key Distribution over a Collective-Noise Channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

F.-G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69, 052319 (2004).
[Crossref]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical Controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

H.-Y. Dai, P.-X. Chen, and C.-Z. Li, “Probabilistic teleportation of an arbitrary two-particle state by a partially entangled three-particle GHZ state and W state,” Opt. Commun. 231, 281–287 (2004).
[Crossref]

2003 (2)

F.-G. Deng, G. L. Long, and X.-S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[Crossref]

F.-G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[Crossref]

2002 (2)

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

1999 (1)

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

1994 (1)

G. M. D’Ariano, “A group-theoretical approach to the quantum damped oscillator,” Phys. Lett. A 187, 231–235 (1994).
[Crossref]

1993 (1)

U. Leonhardt, “Quantum statistics of a lossless beam splitter: SU(2) symmetry in phase space,” Phys. Rev. A 48, 3265–3277 (1993).
[Crossref] [PubMed]

1992 (2)

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

1991 (1)

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

1989 (1)

G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989).
[Crossref] [PubMed]

Bai, J.

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

Barrett, S. D.

S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
[Crossref]

Bartkowiak, M.

M. Bartkowiak, L.-A. Wu, and A. Miranowicz, “Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing,” J. Phys. B 47, 145501 (2014).
[Crossref]

Beausoleil, R. G.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
[Crossref]

Bennett, C. H.

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. - IEEE Int. Conf. comput, Syst. Signal Process., Bangalore, India (IEEE, New York), (1984), pp. 175–179.

Bergou, J.

B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[Crossref]

Bergou, J. A.

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
[Crossref]

Berthiaume, A.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Boileau, J.-C.

J.-C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. Spekkens, “Robust Polarization-Based Quantum Key Distribution over a Collective-Noise Channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. - IEEE Int. Conf. comput, Syst. Signal Process., Bangalore, India (IEEE, New York), (1984), pp. 175–179.

Bužek, V.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Cai, Q.-Y.

Q.-Y. Cai, “Eavesdropping on the two-way quantum communication protocols with invisible photons,” Phys. Lett. A 351, 23–25 (2006).
[Crossref]

Cao, W.-C.

Y. Zhang, W.-C. Cao, and G.-L. Long, “Creation of Multipartite Entanglement and Entanglement Transfer via Heisenberg Interaction,” Chinese Phys. Lett. 22, 2143–2146 (2005).
[Crossref]

Chen, J. F.

H. Yan and J. F. Chen, “Narrowband polarization entangled paired photons with controllable temporal length,” Sci. China Phys. Mech. 58, 074201 (2015).
[Crossref]

Chen, P.-X.

H.-Y. Dai, P.-X. Chen, L.-M. Liang, and C.-Z. Li, “Classical communication cost and remote preparation of the four-particle GHZ class state,” Phys. Lett. A 355, 285–288 (2006).
[Crossref]

H.-Y. Dai, P.-X. Chen, and C.-Z. Li, “Probabilistic teleportation of an arbitrary two-particle state by a partially entangled three-particle GHZ state and W state,” Opt. Commun. 231, 281–287 (2004).
[Crossref]

Cheng, L.-Y.

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

Cui, W.-X.

D’Ariano, G. M.

G. M. D’Ariano, “A group-theoretical approach to the quantum damped oscillator,” Phys. Lett. A 187, 231–235 (1994).
[Crossref]

Dai, H.-Y.

H.-Y. Dai, M. Zhang, and L.-M. Kuang, “Classical Communication Cost and Remote Preparation of Multi-qubit with Three-Party,” Commun. Theor. Phys. 50, 73–76 (2008).
[Crossref]

H.-Y. Dai, P.-X. Chen, L.-M. Liang, and C.-Z. Li, “Classical communication cost and remote preparation of the four-particle GHZ class state,” Phys. Lett. A 355, 285–288 (2006).
[Crossref]

H.-Y. Dai, P.-X. Chen, and C.-Z. Li, “Probabilistic teleportation of an arbitrary two-particle state by a partially entangled three-particle GHZ state and W state,” Opt. Commun. 231, 281–287 (2004).
[Crossref]

Delsing, P.

I.-C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial Atom,” Phys. Rev. Lett. 111, 053601 (2013).
[Crossref] [PubMed]

Deng, F.-G.

F.-G. Deng, B.-C. Ren, and X.-H. Li, “Quantum hyperentanglement and its applications in quantum information processing,” Sci. Bull. 62, 46–68 (2017).
[Crossref]

Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

Y.-B. Sheng and F.-G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[Crossref]

G.-l. Long, F.-g. Deng, C. Wang, X.-h. Li, K. Wen, and W.-y. Wang, “Quantum secure direct communication and deterministic secure quantum communication,” Front. Phys. China 2, 251–272 (2007).
[Crossref]

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A 74, 054302 (2006).
[Crossref]

F.-G. Deng, X.-H. Li, H.-Y. Zhou, and Z.-j. Zhang, “Improving the security of multiparty quantum secret sharing against Trojan horse attack,” Phys. Rev. A 72, 044302 (2005).
[Crossref]

F.-G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69, 052319 (2004).
[Crossref]

F.-G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[Crossref]

F.-G. Deng, G. L. Long, and X.-S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[Crossref]

Ding, D.-S.

W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum Secure Direct Communication with Quantum Memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

Dong, C.-H.

Dong, H.-K.

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

X.-M. Xiu, Q.-Y. Li, Y.-F. Lin, H.-K. Dong, L. Dong, and Y.-J. Gao, “Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities,” Phys. Rev. A 94, 042321 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016).
[Crossref] [PubMed]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-P. Ren, and Y.-J. Gao, “Quantum secure direct communication against the collective noise with polarization-entangled Bell states,” Prog. Theor. Exp. Phys. 2015, 123A02 (2015).
[Crossref]

Dong, L.

X.-M. Xiu, Q.-Y. Li, Y.-F. Lin, H.-K. Dong, L. Dong, and Y.-J. Gao, “Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities,” Phys. Rev. A 94, 042321 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016).
[Crossref] [PubMed]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-P. Ren, and Y.-J. Gao, “Quantum secure direct communication against the collective noise with polarization-entangled Bell states,” Prog. Theor. Exp. Phys. 2015, 123A02 (2015).
[Crossref]

L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014).
[Crossref]

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Two-party quantum privacy comparison with polarization-entangled Bell states and the coherent states,” Quantum Inf. Comput. 14, 0236–0254 (2014).

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules,” Prog. Theor. Exp. Phys. 2013, 093A01 (2013).
[Crossref]

L. Dong, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel,” J. Exp. Theor. Phys. 113, 583–591 (2011).
[Crossref]

Ekert, A. K.

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

Fan, B.

I.-C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial Atom,” Phys. Rev. Lett. 111, 053601 (2013).
[Crossref] [PubMed]

Fan, Q.-B.

A.-D. Zhu, Y. Xia, Q.-B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

Fu, C.-B.

C.-B. Fu, Y. Xia, B.-X. Liu, S. Zhang, K.-H. Yeon, and C.-I. Um, “Controlled Quantum Dense Coding in a Four-particle Non-maximally Entangled State via Local Measurements,” J. Korean Phys. Soc. 46, 1080–1082 (2006).

Y. Xia, C.-B. Fu, F.-Y. Li, and S. Zhang, “Controlled Secure Direct Communication by Using GHZ Entangled State,” J. Korean Phys. Soc. 47, 753–756 (2005).

Gaddam, V.

Gao, F.

S.-J. Qin, F. Gao, F.-Z. Guo, and Q.-Y. Wen, “Comment on ‘Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair’,” Phys. Rev. A 82, 36301 (2010).
[Crossref]

F. Gao, Q.-Y. Wen, and F.-C. Zhu, “Comment on: ‘Quantum exam’ [Phys. Lett. A 350 (2006) 174],” Phys. Lett. A 360, 748–750 (2007).
[Crossref]

Gao, Y.-J.

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

X.-M. Xiu, Q.-Y. Li, Y.-F. Lin, H.-K. Dong, L. Dong, and Y.-J. Gao, “Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities,” Phys. Rev. A 94, 042321 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016).
[Crossref] [PubMed]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-P. Ren, and Y.-J. Gao, “Quantum secure direct communication against the collective noise with polarization-entangled Bell states,” Prog. Theor. Exp. Phys. 2015, 123A02 (2015).
[Crossref]

L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014).
[Crossref]

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Two-party quantum privacy comparison with polarization-entangled Bell states and the coherent states,” Quantum Inf. Comput. 14, 0236–0254 (2014).

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules,” Prog. Theor. Exp. Phys. 2013, 093A01 (2013).
[Crossref]

L. Dong, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel,” J. Exp. Theor. Phys. 113, 583–591 (2011).
[Crossref]

Ghose, S.

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

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W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum Secure Direct Communication with Quantum Memory,” Phys. Rev. Lett. 118, 220501 (2017).
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W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum Secure Direct Communication with Quantum Memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

Shimamura, J.

T. Yamamoto, J. Shimamura, S. K. Özdemir, M. Koashi, and N. Imoto, “Faithful Qubit Distribution Assisted by One Additional Qubit against Collective Noise,” Phys. Rev. Lett. 95, 040503 (2005).
[Crossref] [PubMed]

Song, H.-S.

Y. Xia and H.-S. Song, “Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding,” Phys. Lett. A 364, 117–122 (2007).
[Crossref]

Song, T. T.

K. J. Zhang, L. Zhang, T. T. Song, and Y. H. Yang, “A potential application in quantum networks-Deterministic quantum operation sharing schemes with Bell states,” Sci. China Phys. Mech. 59, 660302 (2016).
[Crossref]

Spekkens, R.

J.-C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. Spekkens, “Robust Polarization-Based Quantum Key Distribution over a Collective-Noise Channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

Spiller, T. P.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
[Crossref]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[Crossref]

Stace, T. M.

I.-C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial Atom,” Phys. Rev. Lett. 111, 053601 (2013).
[Crossref] [PubMed]

Szameit, A.

R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96–100 (2015).
[Crossref]

Tang, C.-j.

J. Wang, Q. Zhang, and C.-j. Tang, “Multiparty controlled quantum secure direct communication using Greenberger-Horne-Zeilinger state,” Opt. Commun. 266, 732–737 (2006).
[Crossref]

Tang, H. X.

W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, “High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits,” Nat. commun. 3, 1325 (2012).
[Crossref] [PubMed]

Tang, S.-Q.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger-Horne-Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Tornberg, L.

I.-C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial Atom,” Phys. Rev. Lett. 111, 053601 (2013).
[Crossref] [PubMed]

Um, C.-I.

C.-B. Fu, Y. Xia, B.-X. Liu, S. Zhang, K.-H. Yeon, and C.-I. Um, “Controlled Quantum Dense Coding in a Four-particle Non-maximally Entangled State via Local Measurements,” J. Korean Phys. Soc. 46, 1080–1082 (2006).

Wang, C.

C. Wang, W.-W. Shen, S.-C. Mi, Y. Zhang, and T.-J. Wang, “Concentration and distribution of entanglement based on valley qubits system in graphene,” Sci. Bull. 60, 2016–2021 (2015).
[Crossref]

G.-l. Long, F.-g. Deng, C. Wang, X.-h. Li, K. Wen, and W.-y. Wang, “Quantum secure direct communication and deterministic secure quantum communication,” Front. Phys. China 2, 251–272 (2007).
[Crossref]

Wang, H.-F.

W.-X. Cui, S. Hu, H.-F. Wang, A.-D. Zhu, and S. Zhang, “Deterministic conversion of a four-photon GHZ state to a W state via homodyne measurement,” Opt. Express 24, 15319 (2016).
[Crossref] [PubMed]

H.-F. Wang, A.-D. Zhu, and S. Zhang, “Physical optimization of quantum error correction circuits with spatially separated quantum dot spins,” Opt. Express 21, 12484–12494 (2013).
[Crossref] [PubMed]

H.-F. Wang, S. Zhang, A.-D. Zhu, X. X. Yi, and K.-H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
[Crossref]

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

H.-F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009).
[Crossref]

H.-F. Wang and S. Zhang, “Quantum Secure Direct Communication by Using a GHZ State,” J. Korean Phys. Soc. 49, 459–463 (2006).

Wang, J.

J. Wang, Q. Zhang, and C.-j. Tang, “Multiparty controlled quantum secure direct communication using Greenberger-Horne-Zeilinger state,” Opt. Commun. 266, 732–737 (2006).
[Crossref]

Wang, J.-X.

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016).
[Crossref] [PubMed]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-P. Ren, and Y.-J. Gao, “Quantum secure direct communication against the collective noise with polarization-entangled Bell states,” Prog. Theor. Exp. Phys. 2015, 123A02 (2015).
[Crossref]

L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014).
[Crossref]

Wang, L.

Y. Sheng, J. Pan, R. Guo, L. Zhou, and L. Wang, “Efficient N-particle W state concentration with different parity check gates,” Sci. China Phys. Mech. 58, 060301 (2015).
[Crossref]

Wang, T.-J.

C. Wang, W.-W. Shen, S.-C. Mi, Y. Zhang, and T.-J. Wang, “Concentration and distribution of entanglement based on valley qubits system in graphene,” Sci. Bull. 60, 2016–2021 (2015).
[Crossref]

Wang, W.-y.

G.-l. Long, F.-g. Deng, C. Wang, X.-h. Li, K. Wen, and W.-y. Wang, “Quantum secure direct communication and deterministic secure quantum communication,” Front. Phys. China 2, 251–272 (2007).
[Crossref]

Wang, X.-B.

X.-B. Wang, “Fault tolerant quantum key distribution protocol with collective random unitary noise,” Phys. Rev. A 72, 050304(R) (2005).
[Crossref]

Wang, X.-W.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger-Horne-Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[Crossref]

Wen, K.

G.-l. Long, F.-g. Deng, C. Wang, X.-h. Li, K. Wen, and W.-y. Wang, “Quantum secure direct communication and deterministic secure quantum communication,” Front. Phys. China 2, 251–272 (2007).
[Crossref]

Wen, Q.-Y.

S.-J. Qin, F. Gao, F.-Z. Guo, and Q.-Y. Wen, “Comment on ‘Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair’,” Phys. Rev. A 82, 36301 (2010).
[Crossref]

F. Gao, Q.-Y. Wen, and F.-C. Zhu, “Comment on: ‘Quantum exam’ [Phys. Lett. A 350 (2006) 174],” Phys. Lett. A 360, 748–750 (2007).
[Crossref]

Wilson, C. M.

I.-C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial Atom,” Phys. Rev. Lett. 111, 053601 (2013).
[Crossref] [PubMed]

Woo, M. K.

B. K. Park, M. S. Lee, M. K. Woo, Y.-S. Kim, S.-W. Han, and S. Moon, “QKD system with fast active optical path length compensation,” Sci. China Phys. Mech. 60, 060311 (2017).
[Crossref]

Wu, L.-A.

M. Bartkowiak, L.-A. Wu, and A. Miranowicz, “Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing,” J. Phys. B 47, 145501 (2014).
[Crossref]

Xia, Y.

Y. Xia and H.-S. Song, “Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding,” Phys. Lett. A 364, 117–122 (2007).
[Crossref]

C.-B. Fu, Y. Xia, B.-X. Liu, S. Zhang, K.-H. Yeon, and C.-I. Um, “Controlled Quantum Dense Coding in a Four-particle Non-maximally Entangled State via Local Measurements,” J. Korean Phys. Soc. 46, 1080–1082 (2006).

A.-D. Zhu, Y. Xia, Q.-B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

Y. Xia, C.-B. Fu, F.-Y. Li, and S. Zhang, “Controlled Secure Direct Communication by Using GHZ Entangled State,” J. Korean Phys. Soc. 47, 753–756 (2005).

Xiao, L.-T.

J.-Y. Hu, B. Yu, M.-Y. Jing, L.-T. Xiao, S.-T. Jia, G.-Q. Qin, and G.-L. Long, “Experimental quantum secure direct communication with single photons,” Light Sci. Appl. 5, e16144 (2016).
[Crossref]

Xiao, Y.-F.

Xie, L.-J.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger-Horne-Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[Crossref]

Xiu, X.-M.

X.-M. Xiu, Q.-Y. Li, Y.-F. Lin, H.-K. Dong, L. Dong, and Y.-J. Gao, “Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities,” Phys. Rev. A 94, 042321 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016).
[Crossref] [PubMed]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-P. Ren, and Y.-J. Gao, “Quantum secure direct communication against the collective noise with polarization-entangled Bell states,” Prog. Theor. Exp. Phys. 2015, 123A02 (2015).
[Crossref]

L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014).
[Crossref]

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Two-party quantum privacy comparison with polarization-entangled Bell states and the coherent states,” Quantum Inf. Comput. 14, 0236–0254 (2014).

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules,” Prog. Theor. Exp. Phys. 2013, 093A01 (2013).
[Crossref]

L. Dong, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel,” J. Exp. Theor. Phys. 113, 583–591 (2011).
[Crossref]

Yamamoto, T.

T. Yamamoto, J. Shimamura, S. K. Özdemir, M. Koashi, and N. Imoto, “Faithful Qubit Distribution Assisted by One Additional Qubit against Collective Noise,” Phys. Rev. Lett. 95, 040503 (2005).
[Crossref] [PubMed]

Yan, H.

H. Yan and J. F. Chen, “Narrowband polarization entangled paired photons with controllable temporal length,” Sci. China Phys. Mech. 58, 074201 (2015).
[Crossref]

Yang, L.

Yang, Y. H.

K. J. Zhang, L. Zhang, T. T. Song, and Y. H. Yang, “A potential application in quantum networks-Deterministic quantum operation sharing schemes with Bell states,” Sci. China Phys. Mech. 59, 660302 (2016).
[Crossref]

Yeon, K.-H.

H.-F. Wang, S. Zhang, A.-D. Zhu, X. X. Yi, and K.-H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
[Crossref]

C.-B. Fu, Y. Xia, B.-X. Liu, S. Zhang, K.-H. Yeon, and C.-I. Um, “Controlled Quantum Dense Coding in a Four-particle Non-maximally Entangled State via Local Measurements,” J. Korean Phys. Soc. 46, 1080–1082 (2006).

Yi, X. X.

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Two-party quantum privacy comparison with polarization-entangled Bell states and the coherent states,” Quantum Inf. Comput. 14, 0236–0254 (2014).

L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014).
[Crossref]

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules,” Prog. Theor. Exp. Phys. 2013, 093A01 (2013).
[Crossref]

L. Dong, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel,” J. Exp. Theor. Phys. 113, 583–591 (2011).
[Crossref]

H.-F. Wang, S. Zhang, A.-D. Zhu, X. X. Yi, and K.-H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
[Crossref]

Yin, Z. Q.

T. Li and Z. Q. Yin, “Quantum superposition, entanglement, and state teleportation of a microorganism on an electromechanical oscillator,” Sci. Bull. 61, 163–171 (2016).
[Crossref]

Yu, B.

J.-Y. Hu, B. Yu, M.-Y. Jing, L.-T. Xiao, S.-T. Jia, G.-Q. Qin, and G.-L. Long, “Experimental quantum secure direct communication with single photons,” Light Sci. Appl. 5, e16144 (2016).
[Crossref]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Zhang, D.-Y.

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger-Horne-Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[Crossref]

Zhang, K. J.

K. J. Zhang, L. Zhang, T. T. Song, and Y. H. Yang, “A potential application in quantum networks-Deterministic quantum operation sharing schemes with Bell states,” Sci. China Phys. Mech. 59, 660302 (2016).
[Crossref]

Zhang, L.

K. J. Zhang, L. Zhang, T. T. Song, and Y. H. Yang, “A potential application in quantum networks-Deterministic quantum operation sharing schemes with Bell states,” Sci. China Phys. Mech. 59, 660302 (2016).
[Crossref]

Zhang, M.

H.-Y. Dai, M. Zhang, and L.-M. Kuang, “Classical Communication Cost and Remote Preparation of Multi-qubit with Three-Party,” Commun. Theor. Phys. 50, 73–76 (2008).
[Crossref]

Zhang, Q.

J. Wang, Q. Zhang, and C.-j. Tang, “Multiparty controlled quantum secure direct communication using Greenberger-Horne-Zeilinger state,” Opt. Commun. 266, 732–737 (2006).
[Crossref]

Zhang, S.

W.-X. Cui, S. Hu, H.-F. Wang, A.-D. Zhu, and S. Zhang, “Deterministic conversion of a four-photon GHZ state to a W state via homodyne measurement,” Opt. Express 24, 15319 (2016).
[Crossref] [PubMed]

H.-F. Wang, A.-D. Zhu, and S. Zhang, “Physical optimization of quantum error correction circuits with spatially separated quantum dot spins,” Opt. Express 21, 12484–12494 (2013).
[Crossref] [PubMed]

H.-F. Wang, S. Zhang, A.-D. Zhu, X. X. Yi, and K.-H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express 19, 25433–25440 (2011).
[Crossref]

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

H.-F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009).
[Crossref]

C.-B. Fu, Y. Xia, B.-X. Liu, S. Zhang, K.-H. Yeon, and C.-I. Um, “Controlled Quantum Dense Coding in a Four-particle Non-maximally Entangled State via Local Measurements,” J. Korean Phys. Soc. 46, 1080–1082 (2006).

A.-D. Zhu, Y. Xia, Q.-B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

H.-F. Wang and S. Zhang, “Quantum Secure Direct Communication by Using a GHZ State,” J. Korean Phys. Soc. 49, 459–463 (2006).

Y. Xia, C.-B. Fu, F.-Y. Li, and S. Zhang, “Controlled Secure Direct Communication by Using GHZ Entangled State,” J. Korean Phys. Soc. 47, 753–756 (2005).

Zhang, W.

W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum Secure Direct Communication with Quantum Memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

Zhang, Y.

C. Wang, W.-W. Shen, S.-C. Mi, Y. Zhang, and T.-J. Wang, “Concentration and distribution of entanglement based on valley qubits system in graphene,” Sci. Bull. 60, 2016–2021 (2015).
[Crossref]

Y. Zhang, W.-C. Cao, and G.-L. Long, “Creation of Multipartite Entanglement and Entanglement Transfer via Heisenberg Interaction,” Chinese Phys. Lett. 22, 2143–2146 (2005).
[Crossref]

Zhang, Z.-j.

F.-G. Deng, X.-H. Li, H.-Y. Zhou, and Z.-j. Zhang, “Improving the security of multiparty quantum secret sharing against Trojan horse attack,” Phys. Rev. A 72, 044302 (2005).
[Crossref]

Zhao, S.-M.

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

Zheng, B.-Y.

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

Zhou, H.-Y.

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[Crossref]

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A 74, 054302 (2006).
[Crossref]

F.-G. Deng, X.-H. Li, H.-Y. Zhou, and Z.-j. Zhang, “Improving the security of multiparty quantum secret sharing against Trojan horse attack,” Phys. Rev. A 72, 044302 (2005).
[Crossref]

Zhou, L.

W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum Secure Direct Communication with Quantum Memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

C.-C. Qu, L. Zhou, and Y.-B. Sheng, “Entanglement concentration for concatenated Greenberger-Horne-Zeilinger state,” Quantum Inf. Process. 14, 4131–4146 (2015).
[Crossref]

Y. Sheng, J. Pan, R. Guo, L. Zhou, and L. Wang, “Efficient N-particle W state concentration with different parity check gates,” Sci. China Phys. Mech. 58, 060301 (2015).
[Crossref]

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

Zhu, A.-D.

Zhu, F.-C.

F. Gao, Q.-Y. Wen, and F.-C. Zhu, “Comment on: ‘Quantum exam’ [Phys. Lett. A 350 (2006) 174],” Phys. Lett. A 360, 748–750 (2007).
[Crossref]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University, Cambridge, 1997).
[Crossref]

Appl. Phys. Lett. (1)

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[Crossref]

Chinese Phys. Lett. (1)

Y. Zhang, W.-C. Cao, and G.-L. Long, “Creation of Multipartite Entanglement and Entanglement Transfer via Heisenberg Interaction,” Chinese Phys. Lett. 22, 2143–2146 (2005).
[Crossref]

Commun. Theor. Phys. (1)

H.-Y. Dai, M. Zhang, and L.-M. Kuang, “Classical Communication Cost and Remote Preparation of Multi-qubit with Three-Party,” Commun. Theor. Phys. 50, 73–76 (2008).
[Crossref]

Front. Phys. China (1)

G.-l. Long, F.-g. Deng, C. Wang, X.-h. Li, K. Wen, and W.-y. Wang, “Quantum secure direct communication and deterministic secure quantum communication,” Front. Phys. China 2, 251–272 (2007).
[Crossref]

J. Exp. Theor. Phys. (1)

L. Dong, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Controlled quantum key distribution with three-photon polarization-entangled states via the collective noise channel,” J. Exp. Theor. Phys. 113, 583–591 (2011).
[Crossref]

J. Korean Phys. Soc. (3)

H.-F. Wang and S. Zhang, “Quantum Secure Direct Communication by Using a GHZ State,” J. Korean Phys. Soc. 49, 459–463 (2006).

C.-B. Fu, Y. Xia, B.-X. Liu, S. Zhang, K.-H. Yeon, and C.-I. Um, “Controlled Quantum Dense Coding in a Four-particle Non-maximally Entangled State via Local Measurements,” J. Korean Phys. Soc. 46, 1080–1082 (2006).

Y. Xia, C.-B. Fu, F.-Y. Li, and S. Zhang, “Controlled Secure Direct Communication by Using GHZ Entangled State,” J. Korean Phys. Soc. 47, 753–756 (2005).

J. Phys. B (2)

B. He, Y.-H. Ren, and J. A. Bergou, “Universal entangler with photon pairs in arbitrary states,” J. Phys. B 43, 025502 (2010).
[Crossref]

M. Bartkowiak, L.-A. Wu, and A. Miranowicz, “Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing,” J. Phys. B 47, 145501 (2014).
[Crossref]

Light Sci. Appl. (1)

J.-Y. Hu, B. Yu, M.-Y. Jing, L.-T. Xiao, S.-T. Jia, G.-Q. Qin, and G.-L. Long, “Experimental quantum secure direct communication with single photons,” Light Sci. Appl. 5, e16144 (2016).
[Crossref]

Nat. commun. (1)

W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, “High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits,” Nat. commun. 3, 1325 (2012).
[Crossref] [PubMed]

New J. Phys. (1)

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[Crossref]

Opt. Commun. (2)

H.-Y. Dai, P.-X. Chen, and C.-Z. Li, “Probabilistic teleportation of an arbitrary two-particle state by a partially entangled three-particle GHZ state and W state,” Opt. Commun. 231, 281–287 (2004).
[Crossref]

J. Wang, Q. Zhang, and C.-j. Tang, “Multiparty controlled quantum secure direct communication using Greenberger-Horne-Zeilinger state,” Opt. Commun. 266, 732–737 (2006).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Phys. Lett. A (5)

Q.-Y. Cai, “Eavesdropping on the two-way quantum communication protocols with invisible photons,” Phys. Lett. A 351, 23–25 (2006).
[Crossref]

F. Gao, Q.-Y. Wen, and F.-C. Zhu, “Comment on: ‘Quantum exam’ [Phys. Lett. A 350 (2006) 174],” Phys. Lett. A 360, 748–750 (2007).
[Crossref]

G. M. D’Ariano, “A group-theoretical approach to the quantum damped oscillator,” Phys. Lett. A 187, 231–235 (1994).
[Crossref]

H.-Y. Dai, P.-X. Chen, L.-M. Liang, and C.-Z. Li, “Classical communication cost and remote preparation of the four-particle GHZ class state,” Phys. Lett. A 355, 285–288 (2006).
[Crossref]

Y. Xia and H.-S. Song, “Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding,” Phys. Lett. A 364, 117–122 (2007).
[Crossref]

Phys. Rev. A (22)

A.-D. Zhu, Y. Xia, Q.-B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A 73, 022338 (2006).
[Crossref]

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A 74, 054302 (2006).
[Crossref]

F.-G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[Crossref]

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[Crossref]

F.-G. Deng, G. L. Long, and X.-S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A 68, 042317 (2003).
[Crossref]

F.-G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69, 052319 (2004).
[Crossref]

H.-F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009).
[Crossref]

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

X.-B. Wang, “Fault tolerant quantum key distribution protocol with collective random unitary noise,” Phys. Rev. A 72, 050304(R) (2005).
[Crossref]

F.-G. Deng, X.-H. Li, H.-Y. Zhou, and Z.-j. Zhang, “Improving the security of multiparty quantum secret sharing against Trojan horse attack,” Phys. Rev. A 72, 044302 (2005).
[Crossref]

Y.-B. Sheng and F.-G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

Y.-B. Sheng, F.-G. Deng, and G.-L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).
[Crossref]

X.-M. Xiu, Q.-Y. Li, Y.-F. Lin, H.-K. Dong, L. Dong, and Y.-J. Gao, “Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities,” Phys. Rev. A 94, 042321 (2016).
[Crossref]

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-J. Gao, and C. H. Oh, “Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities,” Phys. Rev. A 93, 012308 (2016).
[Crossref]

S.-J. Qin, F. Gao, F.-Z. Guo, and Q.-Y. Wen, “Comment on ‘Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair’,” Phys. Rev. A 82, 36301 (2010).
[Crossref]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).
[Crossref]

Q. Guo, J. Bai, L.-Y. Cheng, X.-Q. Shao, H.-F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
[Crossref]

B. He, Y. Ren, and J. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[Crossref]

S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006).
[Crossref]

H. Jeong, “Quantum computation using weak nonlinearities: Robustness against decoherence,” Phys. Rev. A 73, 052320 (2006).
[Crossref]

U. Leonhardt, “Quantum statistics of a lossless beam splitter: SU(2) symmetry in phase space,” Phys. Rev. A 48, 3265–3277 (1993).
[Crossref] [PubMed]

Phys. Rev. Lett. (9)

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical Controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[Crossref]

I.-C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, “Giant Cross-Kerr Effect for Propagating Microwaves Induced by an Artificial Atom,” Phys. Rev. Lett. 111, 053601 (2013).
[Crossref] [PubMed]

G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989).
[Crossref] [PubMed]

J.-C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. Spekkens, “Robust Polarization-Based Quantum Key Distribution over a Collective-Noise Channel,” Phys. Rev. Lett. 92, 017901 (2004).
[Crossref] [PubMed]

T. Yamamoto, J. Shimamura, S. K. Özdemir, M. Koashi, and N. Imoto, “Faithful Qubit Distribution Assisted by One Additional Qubit against Collective Noise,” Phys. Rev. Lett. 95, 040503 (2005).
[Crossref] [PubMed]

W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum Secure Direct Communication with Quantum Memory,” Phys. Rev. Lett. 118, 220501 (2017).
[Crossref] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[Crossref] [PubMed]

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

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Prog. Theor. Exp. Phys. (2)

L. Dong, J.-X. Wang, Q.-Y. Li, H.-Z. Shen, H.-K. Dong, X.-M. Xiu, Y.-P. Ren, and Y.-J. Gao, “Quantum secure direct communication against the collective noise with polarization-entangled Bell states,” Prog. Theor. Exp. Phys. 2015, 123A02 (2015).
[Crossref]

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules,” Prog. Theor. Exp. Phys. 2013, 093A01 (2013).
[Crossref]

Quantum Inf. Comput. (1)

X.-M. Xiu, L. Dong, H.-Z. Shen, Y.-J. Gao, and X. X. Yi, “Two-party quantum privacy comparison with polarization-entangled Bell states and the coherent states,” Quantum Inf. Comput. 14, 0236–0254 (2014).

Quantum Inf. Process. (3)

X.-W. Wang, D.-Y. Zhang, S.-Q. Tang, and L.-J. Xie, “Nondestructive Greenberger-Horne-Zeilinger-state analyzer,” Quantum Inf. Process. 12, 1065–1075 (2013).
[Crossref]

L. Dong, J.-X. Wang, H.-Z. Shen, D. Li, X.-M. Xiu, Y.-J. Gao, and X. X. Yi, “Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel,” Quantum Inf. Process. 13, 1413–1424 (2014).
[Crossref]

C.-C. Qu, L. Zhou, and Y.-B. Sheng, “Entanglement concentration for concatenated Greenberger-Horne-Zeilinger state,” Quantum Inf. Process. 14, 4131–4146 (2015).
[Crossref]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Sci. Bull. (4)

C. Wang, W.-W. Shen, S.-C. Mi, Y. Zhang, and T.-J. Wang, “Concentration and distribution of entanglement based on valley qubits system in graphene,” Sci. Bull. 60, 2016–2021 (2015).
[Crossref]

F.-G. Deng, B.-C. Ren, and X.-H. Li, “Quantum hyperentanglement and its applications in quantum information processing,” Sci. Bull. 62, 46–68 (2017).
[Crossref]

T. Li and Z. Q. Yin, “Quantum superposition, entanglement, and state teleportation of a microorganism on an electromechanical oscillator,” Sci. Bull. 61, 163–171 (2016).
[Crossref]

R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96–100 (2015).
[Crossref]

Sci. China Phys. Mech. (4)

H. Yan and J. F. Chen, “Narrowband polarization entangled paired photons with controllable temporal length,” Sci. China Phys. Mech. 58, 074201 (2015).
[Crossref]

K. J. Zhang, L. Zhang, T. T. Song, and Y. H. Yang, “A potential application in quantum networks-Deterministic quantum operation sharing schemes with Bell states,” Sci. China Phys. Mech. 59, 660302 (2016).
[Crossref]

Y. Sheng, J. Pan, R. Guo, L. Zhou, and L. Wang, “Efficient N-particle W state concentration with different parity check gates,” Sci. China Phys. Mech. 58, 060301 (2015).
[Crossref]

B. K. Park, M. S. Lee, M. K. Woo, Y.-S. Kim, S.-W. Han, and S. Moon, “QKD system with fast active optical path length compensation,” Sci. China Phys. Mech. 60, 060311 (2017).
[Crossref]

Other (2)

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. - IEEE Int. Conf. comput, Syst. Signal Process., Bangalore, India (IEEE, New York), (1984), pp. 175–179.

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University, Cambridge, 1997).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 An illustration plot for distributing photon Ai and photon Bi of a GHZ state from Charlie to Alice (path A) and Bob (path B) via the collective noise channel. The components PBSA1, PBSA2, PBSB1, and PBSB2 reflect the state |V〉 and transmit the state |H〉. A half wave plate (HWP 45°) where the angle of 45° between the optical axis and horizontal polarization mode |H〉 is set, is inserted into the line, which functions as a NOT gate to realize the state exchange of |H〉 and |V〉.
Fig. 2
Fig. 2 A schematic plot of parity analysis. PBSHV (±)1 and PBSHV (±)2 represent the polarization beam splitter transmitting |H〉 (|+〉) mode and reflecting |V〉 (|−〉) mode. θ and 2θ denote phase shifts occurred on the coherent state |α〉. After the phase modulation −3θ, the measurement on the affected coherent state is performed. According to the measurement outcomes, a phase modulation 2ϕ is performed to eliminate the phase difference of one scenario (photons (1,2) pass through path 1′) and another scenario (photons (1,2) pass through path 2′), if the measurement witnesses the existence of nonzero phase shift.
Fig. 3
Fig. 3 The error rates of two protocols. The dimensionless parameters are set as: the practicable phase shift is 20° [60] and the efficiency of detectors is ηd = 91% [61]. The error rate of the first protocol and the error rate of the second protocol are plotted in the red dotted line and the blue solid line respectively, which vary with the amplitude of the coherent state.

Tables (2)

Tables Icon

Table 1 The relations among the outcomes of measurement performed by three participants and the secret information: Charlie’s measurement outcomes ({|+〉, |−〉}) on the control photons Cc and the corresponding publicized information (C. M. Os.), Alice’s parity analysis outcomes and the corresponding publicized information (A. P. A. Os.), Bob’s single-photon measurement outcomes (B. S. P. M. Os.), and the obtained secret information (S. I.).

Tables Icon

Table 2 The relations among Charlie’s single-photon measurement outcomes (C. S.P.M.Os.), Alice’s encoding operations (A. E.Os.), the resulted states (R.Ss.), Bob’s double parity analysis outcomes (B. D.P.A.Os.), and the secret information (S.I.) sent from Alice.

Equations (14)

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| GHZ A i B i C i = 1 2 ( | H H H + | V V V ) A i B i C i ,
1 2 ( | H H A i B i | C A 2 C B 2 | H C i + | V V A i B i | C A 1 C B 1 | V C i ) ,
1 2 | H H A i B i ( | H C i | C A 2 C B 2 + | V C i | C A 1 C B 1 ) .
ρ = ρ 1 ρ 2 , ρ 1 = | H H A i B i H H | , ρ 2 = 1 2 ( | H C i | C A 2 C B 2 + | V C i | C A 1 C B 1 ) ( H | C i C A 2 C B 2 | + V | C i C A 1 C B 1 | ) .
ρ 1 = | H H A i B i H H | ρ 1 = k , l , m , n = 1 2 α k l m n | k l A i B i m n | ,
ρ 1 ρ 2 1 2 ( | V C i V | | C A 1 C B 1 C A 1 C B 1 | k , l , m , n = 1 2 α k l m n | k ¯ , l ¯ A i B i m ¯ n ¯ | + | V C i H | | C A 1 C B 1 C A 2 C B 2 | k , l , m , n = 1 2 α k l m n | k ¯ , l ¯ A i B i m ¯ n ¯ | + | H C i V | | C A 2 C B 2 C A 1 C B 1 | k , l , m , n = 1 2 α k l m n | k , l A i B i m ¯ n ¯ | | H C i H | | C A 2 C B 2 C A 2 C B 2 | k , l , m , n = 1 2 α k l m n | k , l A i B i m n | ) ,
1 2 k , l , m , n = 1 2 [ α k l m n | C A k C B l C A m C B n | | V C i V | | k ¯ , l ¯ A i B i m ¯ n ¯ | + | V C i H | | k ¯ , l ¯ A i B i m ¯ n ¯ | + | H C i V | | k , l A i B i m ¯ n ¯ | + | H C i H | | k , l A i B i m n | ] .
1 2 k , l , m , n = 1 2 α k l m n | C A k C B l C A m C B n | ( | H H H + | V V V ) A i B i C i ( H H H | + V V V | ) .
| Even + = 1 2 ( | + + ± | ) , | Odd + = 1 2 ( | + ± | + ) .
I = | + + | + | | , X = | + | + | + | , Y = | + | | + | , Z = | + + | | | ,
| Φ + + = 1 2 ( | + + + | ) , | Φ + = 1 2 ( | + + | ) , | Ψ + + = 1 2 ( | + + | + ) , | Ψ + = 1 2 ( | + | + ) ,
| Even H V = 1 2 ( | H H ± | V V ) , | Odd H V = 1 2 ( | H V ± | V H ) .
P err 1 = 1 2 erfc [ α ( 1 cos θ ) / 2 ] ,
P err 2 = erfc [ α ( 1 cos θ ) / 2 ] .

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