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

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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, 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]

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.-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, 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]

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]

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, 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]

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]

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, “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]

Ghose, S.

Gisin, N.

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

Goltsman, G. N.

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]

Gottesman, D.

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]

Gräfe, M.

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]

Guo, F.-Z.

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]

Guo, G.-C.

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]

Guo, Q.

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]

Guo, R.

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]

Han, S.-W.

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]

He, B.

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

Heilmann, R.

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]

Hillery, M.

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

Hoi, I.-C.

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]

Hu, J.-Y.

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]

Hu, S.

Imoto, N.

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]

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]

Jeong, H.

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

Jia, S.-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).
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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).
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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).
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H.-F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009).
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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, and Y.-J. Gao, “Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem,” Opt. Lett. 41, 1030–1033 (2016).
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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).
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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).
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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).
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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).
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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).
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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).

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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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]

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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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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Zhu, F.-C.

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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).
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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).
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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).
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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).
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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).
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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).

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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).
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Opt. Express (5)

Opt. Lett. (1)

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Phys. Rev. A (22)

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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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