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Logic Bell state concentration with parity check measurement |
Jiu Liu1, Lan Zhou2, Wei Zhong1, Yu-Bo Sheng1,3( ) |
1. Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China 2. School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China 3. Key Lab of Broadband Wireless Communication and Sensor Network Technology (Ministry of Education), Nanjing University of Posts and Telecommunications, Nanjing 210003, China |
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Abstract Logic qubit plays an important role in current quantum communication. In this paper, we propose an efficient entanglement concentration protocol (ECP) for a new kind of logic Bell state, where the logic qubit is the concatenated Greenber–Horne–Zeilinger (C-GHZ) state. Our ECP relies on the nondemolition polarization parity check (PPC) gates constructed with cross-Kerr nonlinearity, and can distill one pair of maximally entangled logic Bell state from two same pairs of less-entangled logic Bell states. Benefit from the nondemolition PPC gates, the concentrated maximally entangled logic Bell state can be remained for further application. Moreover, our ECP can be repeated to further concentrate the less-entangled logic Bell state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in future long-distance quantum communication.
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Keywords
concatenated Greenber–Horne–Zeilinger (C-GHZ) state
single photon
cross-Kerr nonlinearity
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Corresponding Author(s):
Yu-Bo Sheng
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Issue Date: 24 October 2018
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1 |
E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature 409(6816), 46 (2001)
https://doi.org/10.1038/35051009
|
2 |
C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein–Podolsky– Rosen channels, Phys. Rev. Lett. 70(13), 1895 (1993)
https://doi.org/10.1103/PhysRevLett.70.1895
|
3 |
T. C. Li and Z. Q. Yin, Quantum superposition, entanglement, and state teleportation of a microorganism on an electromechanical oscillator, Sci. Bull. 61(2), 163 (2016)
https://doi.org/10.1007/s11434-015-0990-x
|
4 |
M. D. G. Ramírez, B. J. Falaye, G. H. Sun, M. Cruz-Irisson, and S. H. Dong, Quantum teleportation and information splitting via four-qubit cluster state and a Bell state, Front. Phys. 12(5), 120306 (2017)
https://doi.org/10.1007/s11467-017-0684-8
|
5 |
P. Y. Xiong, X. T. Yu, H. T. Zhan, and Z. C. Zhang, Multiple teleportation via partially entangled GHZ state, Front. Phys. 11(4), 110303 (2016)
https://doi.org/10.1007/s11467-016-0553-x
|
6 |
A. K. Ekert, Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67(6), 661 (1991)
https://doi.org/10.1103/PhysRevLett.67.661
|
7 |
D. Y. Cao, B. H. Liu, Z. Wang, Y. F. Huang, C. F. Li, and G. C. Guo, Multiuser-to-multiuser entanglement distribution based on 1550 nm polarization-entangled photons, Sci. Bull. 60(12), 1128 (2015)
https://doi.org/10.1007/s11434-015-0801-4
|
8 |
G. L. Long and X. S. Liu, Theoretically efficient high capacity quantum-key-distribution scheme, Phys. Rev. A 65(3), 032302 (2002)
https://doi.org/10.1103/PhysRevA.65.032302
|
9 |
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(4), 042317 (2003)
https://doi.org/10.1103/PhysRevA.68.042317
|
10 |
C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, Quantum secure direct communication with high dimension quantum superdense coding, Phys. Rev. A 71(4), 044305 (2005)
https://doi.org/10.1103/PhysRevA.71.044305
|
11 |
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(9), e16144 (2016)
https://doi.org/10.1038/lsa.2016.144
|
12 |
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(22), 220501 (2017)
https://doi.org/10.1103/PhysRevLett.118.220501
|
13 |
F. Zhu, W. Zhang, Y. B. Sheng, and Y. D. Huang, Experimental long-distance quantum secret direct communication, Sci. Bull. 62(22), 1519 (2017)
https://doi.org/10.1016/j.scib.2017.10.023
|
14 |
Y. B. Sheng and L. Zhou, Distributed secure quantum machine learning, Sci. Bull. 62(14), 1025 (2017)
https://doi.org/10.1016/j.scib.2017.06.007
|
15 |
X. Q. Shao, T. Y. Zheng, and S. Zhang, Engineering steady three-atom singlet states via quantum-jump based feedback, Phys. Rev. A 85(4), 042308 (2012)
https://doi.org/10.1103/PhysRevA.85.042308
|
16 |
X. Q. Shao, T. Y. Zheng, C. H. Oh, and S. Zhang, Dissipative creation of three-dimensional entangled state in optical cavity via spontaneous emission, Phys. Rev. A 89(1), 012319 (2014)
https://doi.org/10.1103/PhysRevA.89.012319
|
17 |
X. Q. Shao, J. B. You, T. Y. Zheng, C. H. Oh, and S. Zhang, Stationary three-dimensional entanglement via dissipative Rydberg pumping, Phys. Rev. A 89(5), 052313 (2014)
https://doi.org/10.1103/PhysRevA.89.052313
|
18 |
T. Y. Ye, Robust quantum dialogue based on a shared auxiliary logical Bell state against collective noise, Sci. China Phys. Mech. Astron. 58, 040301 (2015)
https://doi.org/10.1360/SSPMA2014-00289
|
19 |
W. Huang, Q. Su, B. J. Xu, B. Liu, F. Fan, H. Y. Jia, and Y. H. Yang, Improved multiparty quantum key agreement in travelling mode, Sci. China Phys. Mech. Astron. 59(12), 120311 (2016)
https://doi.org/10.1007/s11433-016-0322-3
|
20 |
C. J. Liu, W. Ye, W. D. Zhou, H. L. Zhang, J. H. Huang, and L. Y. Hu, Entanglement of coherent superposition of photon-subtraction squeezed vacuum, Front. Phys. 12(5), 120307 (2017)
https://doi.org/10.1007/s11467-017-0694-6
|
21 |
M. Y. Wang, F. L. Yan, and T. Gao, Generation of four photon polarization entangled decoherence-free states with cross-Kerr nonlinearity, Sci. Rep. 6(1), 38233 (2016)
https://doi.org/10.1038/srep38233
|
22 |
A. Farouk, J. Batle, M. Elhoseny, M. Naseri, M. Lone, A. Fedorov, M. Alkhambashi, S. H. Ahmed, and M. Abdel-Aty, Robust general N user authentication scheme in a centralized quantum communication network via generalized GHZ states, Front. Phys. 13(2), 130306 (2018)
https://doi.org/10.1007/s11467-017-0717-3
|
23 |
J. Batle, A. Farouk, O. Tarawneh, and S. Abdalla, Multipartite quantum correlations among atoms in QED cavities,Front. Phys. 13(1), 130305 (2018)
https://doi.org/10.1007/s11467-017-0711-9
|
24 |
C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 76(5), 722 (1996)
https://doi.org/10.1103/PhysRevLett.76.722
|
25 |
W. Dür, H. J. Briegel, J. I. Cirac, and P. Zoller, Quantum repeaters based on entanglement purification, Phys. Rev. A 59(1), 169 (1999)
https://doi.org/10.1103/PhysRevA.59.169
|
26 |
J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, Entanglement purification for quantum communication, Nature 410(6832), 1067 (2001)
https://doi.org/10.1038/35074041
|
27 |
D. Gonţa and P. van Loock, High-fidelity entanglement purification using chains of atoms and optical cavities, Phys. Rev. A 86(5), 052312 (2012)
https://doi.org/10.1103/PhysRevA.86.052312
|
28 |
M. Zwerger, H. J. Briegel, and W. Dür, Universal and optimal error thresholds for measurement-based entanglement purification, Phys. Rev. Lett. 110(26), 260503 (2013)
https://doi.org/10.1103/PhysRevLett.110.260503
|
29 |
M. Zwerger, H. J. Briegel, and W. Dür, Robustness of hashing protocols for entanglement purification, Phys. Rev. A 90(1), 012314 (2014)
https://doi.org/10.1103/PhysRevA.90.012314
|
30 |
J. Z. Bernád, J. M. Torres, L. Kunz, and G. Alber, Multiphoton-state-assisted entanglement purification of material qubits, Phys. Rev. A 93(3), 032317 (2016)
https://doi.org/10.1103/PhysRevA.93.032317
|
31 |
C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Concentrating partial entanglement by local operations, Phys. Rev. A 53(4), 2046 (1996)
https://doi.org/10.1103/PhysRevA.53.2046
|
32 |
S. Bose, V. Vedral, and P. L. Knight, Purification via entanglement swapping and conserved entanglement, Phys. Rev. A 60(1), 194 (1999)
https://doi.org/10.1103/PhysRevA.60.194
|
33 |
T. Yamamoto, M. Koashi, and N. Imoto, Concentration and purification scheme for two partially entangled photon pairs, Phys. Rev. A 64(1), 012304 (2001)
https://doi.org/10.1103/PhysRevA.64.012304
|
34 |
Z. Zhao, J. W. Pan, and M. S. Zhan, Practical scheme for entanglement concentration, Phys. Rev. A 64(1), 014301 (2001)
https://doi.org/10.1103/PhysRevA.64.014301
|
35 |
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(1), 012307 (2012)
https://doi.org/10.1103/PhysRevA.85.012307
|
36 |
F. G. Deng, Optimal nonlocal multipartite entanglement concentration based on projection measurements, Phys. Rev. A 85(2), 022311 (2012)
https://doi.org/10.1103/PhysRevA.85.022311
|
37 |
Y. B. Sheng, L. Zhou, and S. M. Zhao, Efficient two-step entanglement concentration for arbitrary Wstates, Phys. Rev. A 85(4), 042302 (2012)
https://doi.org/10.1103/PhysRevA.85.042302
|
38 |
Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, Atomic and photonic entanglement concentration via photonic Faraday rotation, Phys. Rev. A 86(3), 034305 (2012)
https://doi.org/10.1103/PhysRevA.86.034305
|
39 |
C. Cao, C. Wang, L. Y. He, and R. Zhang, Atomic entanglement purification and concentration using coherent state input-output process in low-Qcavity QED regime, Opt. Express 21(4), 4093 (2013)
https://doi.org/10.1364/OE.21.004093
|
40 |
Y. B. 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. Astron. 58(6), 060301 (2015)
https://doi.org/10.1007/s11433-015-5672-9
|
41 |
M. Y. Wang, F. L. Yan, and J. Z. Xu, Perfect entanglement concentration of an arbitrary four-photon polarization entangled state via quantum nondemolition detectors, J. Phys. B-At. Mol. Opt. 49(15), 155502 (2016)
https://doi.org/10.1088/0953-4075/49/15/155502
|
42 |
C. C. Qu, L. Zhou, and Y. B. Sheng, Entanglement concentration for concatenated Greenberger– Horne–Zeilinger state, Quantum Inform. Process 14(11), 4131 (2015)
https://doi.org/10.1007/s11128-015-1113-y
|
43 |
J. Pan, L. Zhou, S. P. Gu, X. F. Wang, Y. B. Sheng, and Q. Wang, Efficient entanglement concentration for concatenated Greenberger–Horne–Zeilinger state with the cross-Kerr nonlinearity, Quantum Inform. Process 15(4), 1669 (2016)
https://doi.org/10.1007/s11128-016-1246-7
|
44 |
A. M. Steane and B. Ibinson, Fault-tolerant logical gate networks for Calderbank–Shor–Steane codes, Phys. Rev. A 72(5), 052335 (2005)
https://doi.org/10.1103/PhysRevA.72.052335
|
45 |
S. Muralidharan, C. L. Zou, L. S. Li, J. M. Wen, and L. Jiang, Overcoming erasure errors with multilevel systems, New J. Phys. 19(1), 013026 (2017)
https://doi.org/10.1088/1367-2630/aa573a
|
46 |
F. Fröwis and W. Dür, Stable macroscopic quantum superpositions, Phys. Rev. Lett. 106(11), 110402 (2011)
https://doi.org/10.1103/PhysRevLett.106.110402
|
47 |
H. Lu, L. K. Chen, C. Liu, P. Xu, X. C. Yao, L. Li, N. L. Liu, B. Zhao, Y. A. Chen, and J. W. Pan, Experimental realization of a concatenated Greenberger–Horne–Zeilinger state for macroscopic quantum superpositions, Nat. Photonics 8(5), 364 (2014)
https://doi.org/10.1038/nphoton.2014.81
|
48 |
F. Fröwis and W. Dür, Stability of encoded macroscopic quantum superpositions, Phys. Rev. A 85(5), 052329 (2012)
https://doi.org/10.1103/PhysRevA.85.052329
|
49 |
F. Kesting, F. Fröwis, and W. Dür, Effective noise channels for encoded quantum systems, Phys. Rev. A 88(4), 042305 (2013)
https://doi.org/10.1103/PhysRevA.88.042305
|
50 |
D. Ding, F. L. Yan, and T. Gao, Preparation of kmphoton concatenated Greenberger–Horne–Zeilinger states for observing distinctive quantum effects at macroscopic scales, JOSA B 30(11), 3075 (2013)
https://doi.org/10.1364/JOSAB.30.003075
|
51 |
L. Zhou and Y. B. Sheng, Complete logic Bell-state analysis assisted with photonic Faraday rotation, Phys. Rev. A 92(4), 042314 (2015)
https://doi.org/10.1103/PhysRevA.92.042314
|
52 |
Y. B. Sheng and L. Zhou, Two-step complete polarization logic Bell-state analysis, Sci. Rep. 5(1), 13453 (2015)
https://doi.org/10.1038/srep13453
|
53 |
L. Zhou and Y. B. Sheng, Feasible logic Bell-state analysis with linear optics, Sci. Rep. 6(1), 20901 (2016)
https://doi.org/10.1038/srep20901
|
54 |
T. C. Ralph, A. J. F. Hayes, and A. Gilchrist, Losstolerant optical qubits, Phys. Rev. Lett. 95(10), 100501 (2005)
https://doi.org/10.1103/PhysRevLett.95.100501
|
55 |
A. Gilchrist, A. J. F. Hayes, and T. C. Ralph, Efficient parity-encoded optical quantum computing, Phys. Rev. A 75(5), 052328 (2007)
https://doi.org/10.1103/PhysRevA.75.052328
|
56 |
J. Borregaard, A. S. Sørensen, J. I. Cirac, and M. D. Lukin, Efficient quantum computation in a network with probabilistic gates and logical encoding, Phys. Rev. A 95(4), 042312 (2017)
https://doi.org/10.1103/PhysRevA.95.042312
|
57 |
S. Muralidharan, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang, Ultrafast and fault-tolerant quantum communication across long distances, Phys. Rev. Lett. 112(25), 250501 (2014)
https://doi.org/10.1103/PhysRevLett.112.250501
|
58 |
F. Ewert, M. Bergmann, and P. van Loock, Ultrafast long-distance quantum communication with static linear optics, Phys. Rev. Lett. 117(21), 210501 (2016)
https://doi.org/10.1103/PhysRevLett.117.210501
|
59 |
K. Nemoto and W. J. Munro, Nearly deterministic linear optical controlled-not gate, Phys. Rev. Lett. 93(25), 250502 (2004)
https://doi.org/10.1103/PhysRevLett.93.250502
|
60 |
B. He, Q. Lin, and C. Simon, Cross-Kerr nonlinearity between continuous-mode coherent states and single photons, Phys. Rev. A 83(5), 053826 (2011)
https://doi.org/10.1103/PhysRevA.83.053826
|
61 |
Y. Q. He, D. Ding, F. L. Yan, and T. Gao, Exploration of photon-number entangled states using weak nonlinearities, Opt. Express 23(17), 21671 (2015)
https://doi.org/10.1364/OE.23.021671
|
62 |
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(4), 042321 (2016)
https://doi.org/10.1103/PhysRevA.94.042321
|
63 |
L. Dong, Y. F. Yin, C. Cui, H. K. Dong, X. M. Xiu, and Y. J. Gao, Fault-tolerant distribution of GHZ states and controlled DSQC based on parity analyses, Opt. Express 25(16), 18581 (2017)
https://doi.org/10.1364/OE.25.018581
|
64 |
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(5), 1030 (2016)
https://doi.org/10.1364/OL.41.001030
|
65 |
L. Dong, Y. F. Lin, Q. Y. Li, H. K. Dong, X. M. Xiu, and Y. J. Gao, Generation of three-photon polarization entangled decoherence-free states, Ann. Phys. 371, 287 (2016)
https://doi.org/10.1016/j.aop.2016.04.022
|
66 |
P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. 79(1), 135 (2007)
https://doi.org/10.1103/RevModPhys.79.135
|
67 |
G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Observation of quantum state collapse and revival due to the single-photon Kerr effect, Nature 495(7440), 205 (2013)
https://doi.org/10.1038/nature11902
|
68 |
A. Feizpour, M. Hallaji, G. Dmochowski, and A. M. Steinberg, Observation of the nonlinear phase shift due to single post-selected photons, Nat. Phys. 11(11), 905 (2015)
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