Quantum error rejection and fault tolerant quantum communication

Deng Fu-Guo; Li Xi-Han; Li Tao

doi:10.7498/aps.67.20180598

Abstract

Quantum communication utilizes the quantum state as information carrier. The transmission of quantum states is therefore a precondition for various quantum communication protocols. Photons play a central role in quantum communication since they are fast, cheap, easy to control and interact weakly with the environment. However, the widely used polarization degree of freedom of photons is vulnerable to the noise during the transmission. In this article, we review two main methods to deal with the channel noise, i.e., the quantum error rejection scheme and fault tolerant quantum communication. To transmit an arbitrary single-photon state, Li and Deng proposed two faithful state transmission schemes only by resorting to passive linear optics. The success probability can be (2N+1-1)/2N+1 by introducing a wave splitter composed of N unbalance interferometers. Compared with other quantum error rejection schemes, these two scheme are practical both in maneuverability and resource consumption. They are not only suitable for single-photon pure state transmission but also able to be used for transmitting mixed state, which makes them useful for one-way quantum communication. The success probability of error rejection is usually less than 100% since some error cases are rejected. To realize complete fault tolerant quantum communication, decoherence free subspace can be used to encode quantum information. In 2008, Li et al. proposed two efficient quantum key distribution schemes over two different collective-noise channels. The noiseless subspaces are made up of two Bell states and the spatial degree of freedom is introduced to form two nonorthogonal bases. Although entangled states are employed, only single-photon measurements are required to read the information. Later, the scheme is generalized to an efficient one which transmits n-1 bits information via n Einstein-Podolsky-Rosen pairs and many fault tolerant quantum communication schemes were proposed. We compare the practicality of different anti-noise schemes based on maneuverability and resource consumption and a perspective of these two research directions is given in the last section.

Keywords:

Authors and contacts

1.
Department of Physics, Beijing Normal University, Beijing 100875, China;
2.
Department of Physics, Chongqing University, Chongqing 400044, China;
3.
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China

Corresponding author: Deng Fu-Guo, fgdeng@bnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11674033, 11574038).

References

[1]	Bennett C H, Brassard G 1984 Proceedings of International Conference on Computers, System and Signal Processing Bangalore, India, IEEE 175
[2]	Ekert A K 1991 Phys. Rev. Lett. 67 661
[3]	Bennett C H, Brassard G, Mermin N D 1992 Phys. Rev. Lett. 68 557
[4]	Deng F G, Long G L 2003 Phys. Rev. A 68 042315
[5]	Deng F G, Long G L 2004 Phys. Rev. A 70 012311
[6]	Boileau J C, Gottesman D, Laflamme R, Poulin D, Spekkens R W 2004 Phys. Rev. Lett. 92 017901
[7]	Li X H, Deng F G, Zhou H Y 2008 Phys. Rev. A 78 022321
[8]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829
[9]	Karlsson A, Koashi M, Imoto N 1999 Phys. Rev. A 59 162
[10]	Xiao L, Long G L, Deng F G, Pan J W 2004 Phys. Rev. A 69 052307
[11]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302
[12]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317
[13]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319
[14]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305
[15]	Hu J Y, Yu B, Jing M Y, Xiao L T, Jia S T, Qin G Q, Long G L 2016 Light Sci. Appl. 5 e16144
[16]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501
[17]	Zhu F, Zhang W, Sheng Y B, Huang Y 2017 Sci. Bull. 62 1519
[18]	Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[19]	Karlsson A, Bourennane M 1998 Phys. Rev. A 58 4394
[20]	Li X H, Ghose S 2015 Phys. Rev. A 91 012320
[21]	Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[22]	Liu X S, Long G L, Tong D M, Li F 2002 Phys. Rev. A 65 022304
[23]	Stucki D, Ginsin N, Guinnard O, Zbinden H 2002 New. J. Phys. 4 41
[24]	Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[25]	Jones J A, Mosca M, Hansen R H 1998 Nature 393 344
[26]	Long G L, Xiao L 2003 J. Chem. Phys. 119 8473
[27]	Feng G R, Xu G F, Long G L 2013 Phys. Rev. Lett. 110 190501
[28]	Knill E, Laflamme R, Milburn G J 2001 Nature 409 46
[29]	O'Brien J L, Pryde G J, White A G, Ralph T C, Branning D 2003 Nature 426 264
[30]	Duan L M, Kimble H J 2004 Phys. Rev. Lett. 92 127902
[31]	Wei H R, Deng F G 2013 Opt. Express 21 17671
[32]	Song X K, Ai Q, Qiu J, Deng F G 2016 Phys. Rev. A 93 052324
[33]	Song X K, Zhang H, Ai Q, Qiu J, Deng F G 2016 New J. Phys. 18 023001
[34]	Li T, Deng F G 2016 Phys. Rev. A 94 062310
[35]	Li T, Gao J C, Deng F G, Long G L 2018 Ann. Phys. 391 150
[36]	Giovannetti V, Lloyd S, Maccone L 2011 Nature Photon. 5 222
[37]	Jiang L, Taylor J M, Srensen A S, Lukin M D 2007 Phys. Rev. A 76 062323
[38]	Dr W, Briegel H J 2003 Phys. Rev. Lett. 90 067901
[39]	Qin W, Wang X, Miranowicz A, Zhong Z, Nori F 2017 Phys. Rev. A 96 012315
[40]	Kang Y H, Shi Z C, Huang B H, Song J, Xia Y 2017 Ann. Phys. (Berlin) 529 1700154
[41]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025
[42]	Barends R, Kelly J, Megrant A, Veitia A, Sank D, Jeffrey E, White T C, Mutus J, Fowler A G, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth A, Neill C, O'Malley P, Roushan P, Vainsencher A, Wenner J, Korotkov A N, Cleland A N, Martinis J M 2014 Nature 508 500
[43]	Hua M, Tao M J, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. (Berlin) 530 1700402
[44]	Deng F G, Ren B C, Li X H 2017 Sci. Bull. 62 46
[45]	Ren B C, Wei H R, Deng F G 2013 Laser Phys. Lett. 10 095202
[46]	Ren B C, Deng F G 2014 Sci. Rep. 4 4623
[47]	Ren B C, Wang G Y, Deng F G 2015 Phys. Rev. A 91 032328
[48]	Li T, Long G L 2016 Phys. Rev. A 94 022343
[49]	Ren B C, Deng F G 2017 Opt. Express 25 10863
[50]	Wei H R, Deng F G, Long G L 2016 Opt. Express 24 18619
[51]	Ren B C, Deng F G 2015 Acta Phys. Sin. 64 160303 (in Chinese) [任宝藏, 邓富国 2015 64 160303]
[52]	Wang T J, Song S Y, Long G L 2012 Phys. Rev. A 85 062311
[53]	Wang T J, Li T, Du F F, Deng F G 2011 Chin. Phys. Lett. 28 040305
[54]	Gu B, Huang Y G, Fang X, Zhang C Y 2011 Chin. Phys. B 20 100309
[55]	Wu F Z, Yang G J, Wang H B, Xiong J, Alzahrani F, Hobiny A, Deng F G 2017 Sci. China: Phys. Mech. Astron. 60 120313
[56]	Wei T C, Barreiro J T, Kwiat P G 2007 Phys. Rev. A 75 060305
[57]	Sheng Y B, Deng F G, Long G L 2010 Phys. Rev. A 82 032318
[58]	Ren B C, Wei H R, Hua M, Li T, Deng F G 2012 Opt. Express 20 24664
[59]	Wang T J, Lu Y, Long G L 2012 Phys. Rev. A 86 042337
[60]	Liu Q, Zhang M 2015 Phys. Rev. A 91 062321
[61]	Liu Q, Wang G Y, Ai Q, Zhang M, Deng F G 2016 Sci. Rep. 6 22016
[62]	Li X H, Ghose S 2016 Phys. Rev. A 93 022302
[63]	Wang G Y, Ai Q, Ren B C, Li T, Deng F G 2016 Opt. Express 24 28444
[64]	Li X H, Ghose S 2017 Phys. Rev. A 96 020303
[65]	Bennett C H, Bernstein H J, Popescu S, Schumacher B 1996 Phys. Rev. A 53 2046
[66]	Zhao Z, Pan J W, Zhan M S 2001 Phys. Rev. A 64 014301
[67]	Yamamoto T, Koashi M, Imoto N 2001 Phys. Rev. A 64 012304
[68]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 062325
[69]	Ren B C, Du F F, Deng F G 2013 Phys. Rev. A 88 012302
[70]	Sheng Y B, Zhou L, Zhao S M, Zheng B Y 2012 Phys. Rev. A 85 012307
[71]	Deng F G 2012 Phys. Rev. A 85 022311
[72]	Wang C, Zhang Y, Jin G S 2011 Phys. Rev. A 84 032307
[73]	Wang C 2012 Phys. Rev. A 86 012323
[74]	Du F F, Deng F G 2015 Sci. China: Phys. Mech. Astron. 58 040303
[75]	Ren B C, Long G L 2014 Opt. Express 22 6547
[76]	Li X H, Ghose S 2014 Laser Phys. Lett. 11 125201
[77]	Li X H, Ghose S 2015 Opt. Express 23 3550
[78]	Li X H, Ghose S 2015 Phys. Rev. A 91 062302
[79]	Cao C, Wang T J, Mi S C, Zhang R, Wang C 2016 Ann. Phys. 369 128
[80]	Ren B C, Wang H, Alzahrani F, Hobiny A, Deng F G 2017 Ann. Phys. 385 86
[81]	Zhang H, Wang H 2017 Phys. Rev. A 95 052314
[82]	Zhang H, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. 391 112
[83]	Liu H J, Xia Y, Song J 2016 Quantum Inf. Process. 15 2033
[84]	Cao C, Chen X, Duan Y W, Fan L, Zhang R, Wang T J, Wang C 2016 Sci. China: Phys. Mech. Astron. 59 100315
[85]	Sheng Y B, Pan J, Guo R, Zhou L, Wang L 2015 Sci. China: Phys. Mech. Astron. 58 060301
[86]	Zhao R T, Liang R S, Wang F Q 2017 Acta Phys. Sin. 66 240301 (in Chinese) [赵瑞通, 梁瑞生, 王发强 2017 66 240301]
[87]	Zhou L, Sheng Y B 2016 Chin. Phys. B 25 020308
[88]	Guo R, Zhou L, Gu S P, Wang X F, Sheng Y B 2016 Chin. Phys. B 25 030302
[89]	Zhou L, Wang D D, Wang X F, Gu S P, Sheng Y B 2017 Chin. Phys. B 26 020302
[90]	Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, Wootters W K 1996 Phys. Rev. Lett. 76 722
[91]	Pan J W, Simon C, Brukner C, Zellinger A 2001 Nature 410 1067
[92]	Simon C, Pan J W 2002 Phys. Rev. Lett. 89 257901
[93]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 042308
[94]	Deng F G 2011 Phys. Rev. A 84 052312
[95]	Ren B C, Deng F G 2013 Laser Phys. Lett. 10 115201
[96]	Ren B C, Du F F, Deng F G 2014 Phys. Rev. A 90 052309
[97]	Wang G Y, Liu Q, Deng F G 2016 Phys. Rev. A 94 032319
[98]	Du F F, Li T, Long G L 2016 Ann. Phys. 375 105
[99]	Wang G Y, Li T, Ai Q, Alsaedi A, Hayat T, Deng F G 2018 arXiv:1802.00111
[100]	Sheng Y B, Zhou L, Long G L 2013 Phys. Rev. A 88 022302
[101]	Sheng Y B, Zhou L 2015 Sci. Rep. 5 7815
[102]	Zhou L, Sheng Y B 2016 Sci. Rep. 6 28813
[103]	Zhou L, Sheng Y B 2017 Ann. Phys. 385 10
[104]	Wang T J, Liu L L, Zhang R, Cao C, Wang C 2015 Opt. Express 23 9284
[105]	Wang T J, Mi S C, Wang C 2017 Opt. Express 25 2969
[106]	Zhang H, Liu Q, Xu X S, Xiong J, Alsaedi A, Hayat T, Deng F G 2017 Phys. Rev. A 96 052330
[107]	Liu Z C, Hong J S, Guo J J, Li T, Ai Q, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. (Berlin) 530 1800029
[108]	Zhou L, Sheng Y B 2016 Sci. Rep. 6 28813
[109]	Zhou L, Sheng Y B 2017 Ann. Phys. 385 10
[110]	Zhang S S, Shu Q, Zhou L, Sheng Y B 2017 Chin. Phys. B 26 060307
[111]	Sheng Y B, Deng F G 2010 Phys. Rev. A 81 032307
[112]	Li X H 2010 Phys. Rev. A 82 044304
[113]	Sheng Y B, Deng F G 2010 Phys. Rev. A 82 044305
[114]	Deng F G 2011 Phys. Rev. A 83 062316
[115]	Sheng Y B, Zhou L 2014 Laser Phys. Lett. 11 085203
[116]	Li X H, Deng F G, Zhou H Y 2007 Appl. Phys. Lett. 91 144101
[117]	Deng F G, Li X H, Zhou H Y 2011 Quant. Inf. Compu. 11 0913
[118]	Kalamidas D 2005 Phys. Lett. A 343 331
[119]	Yamamoto T, Shimamura J, zdemir S K, Koashi M, Imoto N 2005 Phys. Rev. Lett. 95 040503
[120]	Zanardi P, Rasetii M 1997 Phys. Rev. Lett. 79 3306
[121]	Sun Y 2013 Acta Sin. Quantum Opt. 19 122 (in Chinese) [孙越 2013 量子光学学报 19 122]
[122]	Han C, Zhou Z W, Guo G C 2006 J. Phys. B 39 1677
[123]	Yamamoto T, Nagase R, Shimamura J, zdemir S K, Koashi M, Imoto N 2007 New. J. Phys. 9 191
[124]	Yamamoto T, Hayashi K, zdemir S K, Koashi M, Imoto N 2008 Nat. Photon. 2 488
[125]	Ikuta R, Ono Y, Tashima T, Yamamoto T, Koashi M, Imoto N 2011 Phys. Rev. Lett. 106 110503
[126]	Kumagai H, Yamamoto T, Koashi M, Imoto N 2013 Phys. Rev. A 87 052325
[127]	Li X H, Deng F G, Zhou H Y 2009 Opt. Commun. 282 4025
[128]	Dong L, Xiu X M, Gao Y J, Chi F 2010 Commun. Theor. Phys. 54 269
[129]	Dong L, Wang J X, Shen H Z, Li D, Xiu X M, Gao Y J, Yi X X 2014 Quant. Inf. Process. 13 1413
[130]	Gao M, Liang L M, Li C Z, Tian C L 2006 Phys. Lett. A 359 126
[131]	Sheng Y B, Deng F G 2010 Phys. Rev. A 81 042332
[132]	Niu H C, Ren B C, Wang T J, Hua M, Deng F G 2012 Int. J. Theor. Phys. 51 2346
[133]	Li Y, Chen X, Zeng Z, Li X H 2013 Commun. Theor. Phys. 59 32
[134]	Chen X, Li Y, Zeng Z, Li X H 2013 Commun. Theor. Phys. 60 421
[135]	Kang Y H, Xia Y, Lu P M 2014 Appl. Phys. B 116 977
[136]	Zeng Z, Wang C, Li X H, Wei H 2015 Laser Phys. Lett. 12 015201
[137]	Zhang Z J 2006 Physica A 361 233
[138]	Li X H, Deng F G, Zhou H Y 2009 Int. J. Quantum Inf. 7 1479
[139]	Li C Y, Li Y S 2010 Int. J. Quantum Inf. 8 1101
[140]	Xiu X M, Dong L, Gao Y J, Chi F 2009 Opt. Commun. 282 4171
[141]	Lin S, Guo G D, Gao F, Liu X F 2014 Quant. Inf. Comput. 14 0845
[142]	Lai H, Orgun M A, Xiao J H, Xue L Y 2014 Quant. Inf. Process. 13 1523
[143]	Yuan H, Song J, He Q, Han L F, Hou K, Hu X Y, Shi S H 2008 Commun. Theor. Phys. 50 627
[144]	Gu B, Pei S X, Song B, Zhong K 2009 Sci. China: Phys. Mech. Astron. 52 1913
[145]	Dong L, Xiu X M, Gao Y J, Chi F 2009 Opt. Commun. 282 1688
[146]	Dong H K, Dong L, Xiu X M, Gao Y J 2010 Int. J. Quantum Inf. 8 1389
[147]	Yang C W, Tsai C W, Hwang T 2013 Quant. Inf. Process. 12 3043
[148]	Yang C W, Hwang T 2013 Quant. Inf. Process. 12 3495
[149]	Yuan H, Zhang Q, Hong L, Yin W J, Xu D 2014 Int. J. Theor. Phys. 53 2565
[150]	Wang C, Liu J W, Chen X B, Bi Y G, Shang T 2015 Chin. Phys. B 24 040304
[151]	Gu B, Mu L, Ding L, Zhang C, Li C 2010 Opt. Commun. 283 3099
[152]	Li C Y, Li Y S 2011 Chin. Phys. Lett. 28 020304
[153]	Gu B, Zhang C Y, Cheng G S, Huang Y G 2011 Sci. China: Phys. Mech. Astron. 54 942
[154]	Yang C W, Tsai C W, Hwang T 2011 Sci. China: Phys. Mech. Astron. 54 496
[155]	Yang C W, Hwang T 2012 Int. J. Theor. Phys. 51 3941
[156]	Huang W, Wen Q Y, Jia H Y, Qin S J, Gao F 2012 Chin. Phys. B 21 100308
[157]	Yang C W, Tsai C W, Hwang T 2014 Laser Phys. 24 105203
[158]	Yang C W, Hwang T 2013 Quant. Inf. Process. 12 2131
[159]	Ye T Y 2015 Quant. Inf. Process. 14 1487
[160]	Aolita L, Walborn S P 2007 Phys. Rev. Lett. 98 100501
[161]	Souza C E R, Borges C V S, Khoury A Z 2008 Phys. Rev. A 77 032345
[162]	Yamamoto T, Nagase R, Shimamura J, zdemir S K, Koashi M, Imoto N 2007 New J. Phys. 9 191
[163]	Yamamoto T, Hayashi K, zdemir S K, Koashi M, Imoto N 2008 Nature Photon. 2 488
[164]	Li T, Wang G Y, Deng F G, Long G L 2016 Sci. Rep. 6 20677
[165]	Gao C Y, Wang G Y, Zhang H, Deng F G 2017 Quantum Inf. Process. 16 11
[166]	Jiang Y X, Guo P L, Gao C Y, Wang H B, Alzahrani F, Hobiny A, Deng F G 2017 Sci. China: Phys. Mech. Astron. 60 120312
[167]	Gisin N, Pironio S, Sangouard N 2010 Phys. Rev. Lett. 105 070501
[168]	Bruno N, Pini V, Martin A, Verma V B, Nam S W, Mirin R, Lita A, Marsili F, Krozh B, Bussires F, Sangouard N, Zbinden H, Gisin N, Thew R 2016 Opt. Express 24 125
[169]	Meyer-Scott E, Bula M, Bartkiewicz K, Cernoch A, Soubusta J, Jennewein T, Lemr K 2013 Phys. Rev. A 88 012327
[170]	Zhou L, Sheng Y B 2015 Laser Phys. Lett. 12 045203
[171]	Ouyang Y, Feng Z F, Zhou L, Sheng Y B 2015 Quant. Inf. Process. 14 635
[172]	Ouyang Y, Feng Z F, Zhou L, Sheng Y B 2016 Laser Phys. 26 015204
[173]	Walborn S P, Souto Ribeiro P H, Davidovich L, Mintert F, Buchleitner A 2006 Nature 440 1022
[174]	Lee S M, Ji S W, Lee H W, Zubairy M S 2008 Phys. Rev. A 77 040301
[175]	Zhou L, Sheng Y B 2014 Phys. Rev. A 90 024301
[176]	Sheng Y B, Guo R, Pan J, Zhou L, Wang X F 2015 Quant. Inf. Process. 14 963
[177]	Zhou L, Sheng Y B 2015 Entropy 17 4293
[178]	Zwerger M, Briegel H J, Dr W 2013 Phys. Rev. Lett. 110 260503
[179]	Zwerger M, Briegel H J, Dr W 2014 Phys. Rev. A 90 012314
[180]	Sheng Y B, Zhou L 2016 Sci. Rep. 5 13453
[181]	Zhou L, Sheng Y B 2015 Phys. Rev. A 92 042314
[182]	Lloyd S, Mohseni M, Rebentrost P 2013 arXiv: 1307.0411
[183]	Rebentrost P, Mohseni M, Lloyd S 2014 Phys. Rev. Lett. 113 130503
[184]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025

Cited By

[1]	Bennett C H, Brassard G 1984 Proceedings of International Conference on Computers, System and Signal Processing Bangalore, India, IEEE 175
[2]	Ekert A K 1991 Phys. Rev. Lett. 67 661
[3]	Bennett C H, Brassard G, Mermin N D 1992 Phys. Rev. Lett. 68 557
[4]	Deng F G, Long G L 2003 Phys. Rev. A 68 042315
[5]	Deng F G, Long G L 2004 Phys. Rev. A 70 012311
[6]	Boileau J C, Gottesman D, Laflamme R, Poulin D, Spekkens R W 2004 Phys. Rev. Lett. 92 017901
[7]	Li X H, Deng F G, Zhou H Y 2008 Phys. Rev. A 78 022321
[8]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829
[9]	Karlsson A, Koashi M, Imoto N 1999 Phys. Rev. A 59 162
[10]	Xiao L, Long G L, Deng F G, Pan J W 2004 Phys. Rev. A 69 052307
[11]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302
[12]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317
[13]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319
[14]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305
[15]	Hu J Y, Yu B, Jing M Y, Xiao L T, Jia S T, Qin G Q, Long G L 2016 Light Sci. Appl. 5 e16144
[16]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501
[17]	Zhu F, Zhang W, Sheng Y B, Huang Y 2017 Sci. Bull. 62 1519
[18]	Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[19]	Karlsson A, Bourennane M 1998 Phys. Rev. A 58 4394
[20]	Li X H, Ghose S 2015 Phys. Rev. A 91 012320
[21]	Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[22]	Liu X S, Long G L, Tong D M, Li F 2002 Phys. Rev. A 65 022304
[23]	Stucki D, Ginsin N, Guinnard O, Zbinden H 2002 New. J. Phys. 4 41
[24]	Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[25]	Jones J A, Mosca M, Hansen R H 1998 Nature 393 344
[26]	Long G L, Xiao L 2003 J. Chem. Phys. 119 8473
[27]	Feng G R, Xu G F, Long G L 2013 Phys. Rev. Lett. 110 190501
[28]	Knill E, Laflamme R, Milburn G J 2001 Nature 409 46
[29]	O'Brien J L, Pryde G J, White A G, Ralph T C, Branning D 2003 Nature 426 264
[30]	Duan L M, Kimble H J 2004 Phys. Rev. Lett. 92 127902
[31]	Wei H R, Deng F G 2013 Opt. Express 21 17671
[32]	Song X K, Ai Q, Qiu J, Deng F G 2016 Phys. Rev. A 93 052324
[33]	Song X K, Zhang H, Ai Q, Qiu J, Deng F G 2016 New J. Phys. 18 023001
[34]	Li T, Deng F G 2016 Phys. Rev. A 94 062310
[35]	Li T, Gao J C, Deng F G, Long G L 2018 Ann. Phys. 391 150
[36]	Giovannetti V, Lloyd S, Maccone L 2011 Nature Photon. 5 222
[37]	Jiang L, Taylor J M, Srensen A S, Lukin M D 2007 Phys. Rev. A 76 062323
[38]	Dr W, Briegel H J 2003 Phys. Rev. Lett. 90 067901
[39]	Qin W, Wang X, Miranowicz A, Zhong Z, Nori F 2017 Phys. Rev. A 96 012315
[40]	Kang Y H, Shi Z C, Huang B H, Song J, Xia Y 2017 Ann. Phys. (Berlin) 529 1700154
[41]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025
[42]	Barends R, Kelly J, Megrant A, Veitia A, Sank D, Jeffrey E, White T C, Mutus J, Fowler A G, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth A, Neill C, O'Malley P, Roushan P, Vainsencher A, Wenner J, Korotkov A N, Cleland A N, Martinis J M 2014 Nature 508 500
[43]	Hua M, Tao M J, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. (Berlin) 530 1700402
[44]	Deng F G, Ren B C, Li X H 2017 Sci. Bull. 62 46
[45]	Ren B C, Wei H R, Deng F G 2013 Laser Phys. Lett. 10 095202
[46]	Ren B C, Deng F G 2014 Sci. Rep. 4 4623
[47]	Ren B C, Wang G Y, Deng F G 2015 Phys. Rev. A 91 032328
[48]	Li T, Long G L 2016 Phys. Rev. A 94 022343
[49]	Ren B C, Deng F G 2017 Opt. Express 25 10863
[50]	Wei H R, Deng F G, Long G L 2016 Opt. Express 24 18619
[51]	Ren B C, Deng F G 2015 Acta Phys. Sin. 64 160303 (in Chinese) [任宝藏, 邓富国 2015 64 160303]
[52]	Wang T J, Song S Y, Long G L 2012 Phys. Rev. A 85 062311
[53]	Wang T J, Li T, Du F F, Deng F G 2011 Chin. Phys. Lett. 28 040305
[54]	Gu B, Huang Y G, Fang X, Zhang C Y 2011 Chin. Phys. B 20 100309
[55]	Wu F Z, Yang G J, Wang H B, Xiong J, Alzahrani F, Hobiny A, Deng F G 2017 Sci. China: Phys. Mech. Astron. 60 120313
[56]	Wei T C, Barreiro J T, Kwiat P G 2007 Phys. Rev. A 75 060305
[57]	Sheng Y B, Deng F G, Long G L 2010 Phys. Rev. A 82 032318
[58]	Ren B C, Wei H R, Hua M, Li T, Deng F G 2012 Opt. Express 20 24664
[59]	Wang T J, Lu Y, Long G L 2012 Phys. Rev. A 86 042337
[60]	Liu Q, Zhang M 2015 Phys. Rev. A 91 062321
[61]	Liu Q, Wang G Y, Ai Q, Zhang M, Deng F G 2016 Sci. Rep. 6 22016
[62]	Li X H, Ghose S 2016 Phys. Rev. A 93 022302
[63]	Wang G Y, Ai Q, Ren B C, Li T, Deng F G 2016 Opt. Express 24 28444
[64]	Li X H, Ghose S 2017 Phys. Rev. A 96 020303
[65]	Bennett C H, Bernstein H J, Popescu S, Schumacher B 1996 Phys. Rev. A 53 2046
[66]	Zhao Z, Pan J W, Zhan M S 2001 Phys. Rev. A 64 014301
[67]	Yamamoto T, Koashi M, Imoto N 2001 Phys. Rev. A 64 012304
[68]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 062325
[69]	Ren B C, Du F F, Deng F G 2013 Phys. Rev. A 88 012302
[70]	Sheng Y B, Zhou L, Zhao S M, Zheng B Y 2012 Phys. Rev. A 85 012307
[71]	Deng F G 2012 Phys. Rev. A 85 022311
[72]	Wang C, Zhang Y, Jin G S 2011 Phys. Rev. A 84 032307
[73]	Wang C 2012 Phys. Rev. A 86 012323
[74]	Du F F, Deng F G 2015 Sci. China: Phys. Mech. Astron. 58 040303
[75]	Ren B C, Long G L 2014 Opt. Express 22 6547
[76]	Li X H, Ghose S 2014 Laser Phys. Lett. 11 125201
[77]	Li X H, Ghose S 2015 Opt. Express 23 3550
[78]	Li X H, Ghose S 2015 Phys. Rev. A 91 062302
[79]	Cao C, Wang T J, Mi S C, Zhang R, Wang C 2016 Ann. Phys. 369 128
[80]	Ren B C, Wang H, Alzahrani F, Hobiny A, Deng F G 2017 Ann. Phys. 385 86
[81]	Zhang H, Wang H 2017 Phys. Rev. A 95 052314
[82]	Zhang H, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. 391 112
[83]	Liu H J, Xia Y, Song J 2016 Quantum Inf. Process. 15 2033
[84]	Cao C, Chen X, Duan Y W, Fan L, Zhang R, Wang T J, Wang C 2016 Sci. China: Phys. Mech. Astron. 59 100315
[85]	Sheng Y B, Pan J, Guo R, Zhou L, Wang L 2015 Sci. China: Phys. Mech. Astron. 58 060301
[86]	Zhao R T, Liang R S, Wang F Q 2017 Acta Phys. Sin. 66 240301 (in Chinese) [赵瑞通, 梁瑞生, 王发强 2017 66 240301]
[87]	Zhou L, Sheng Y B 2016 Chin. Phys. B 25 020308
[88]	Guo R, Zhou L, Gu S P, Wang X F, Sheng Y B 2016 Chin. Phys. B 25 030302
[89]	Zhou L, Wang D D, Wang X F, Gu S P, Sheng Y B 2017 Chin. Phys. B 26 020302
[90]	Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, Wootters W K 1996 Phys. Rev. Lett. 76 722
[91]	Pan J W, Simon C, Brukner C, Zellinger A 2001 Nature 410 1067
[92]	Simon C, Pan J W 2002 Phys. Rev. Lett. 89 257901
[93]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 042308
[94]	Deng F G 2011 Phys. Rev. A 84 052312
[95]	Ren B C, Deng F G 2013 Laser Phys. Lett. 10 115201
[96]	Ren B C, Du F F, Deng F G 2014 Phys. Rev. A 90 052309
[97]	Wang G Y, Liu Q, Deng F G 2016 Phys. Rev. A 94 032319
[98]	Du F F, Li T, Long G L 2016 Ann. Phys. 375 105
[99]	Wang G Y, Li T, Ai Q, Alsaedi A, Hayat T, Deng F G 2018 arXiv:1802.00111
[100]	Sheng Y B, Zhou L, Long G L 2013 Phys. Rev. A 88 022302
[101]	Sheng Y B, Zhou L 2015 Sci. Rep. 5 7815
[102]	Zhou L, Sheng Y B 2016 Sci. Rep. 6 28813
[103]	Zhou L, Sheng Y B 2017 Ann. Phys. 385 10
[104]	Wang T J, Liu L L, Zhang R, Cao C, Wang C 2015 Opt. Express 23 9284
[105]	Wang T J, Mi S C, Wang C 2017 Opt. Express 25 2969
[106]	Zhang H, Liu Q, Xu X S, Xiong J, Alsaedi A, Hayat T, Deng F G 2017 Phys. Rev. A 96 052330
[107]	Liu Z C, Hong J S, Guo J J, Li T, Ai Q, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. (Berlin) 530 1800029
[108]	Zhou L, Sheng Y B 2016 Sci. Rep. 6 28813
[109]	Zhou L, Sheng Y B 2017 Ann. Phys. 385 10
[110]	Zhang S S, Shu Q, Zhou L, Sheng Y B 2017 Chin. Phys. B 26 060307
[111]	Sheng Y B, Deng F G 2010 Phys. Rev. A 81 032307
[112]	Li X H 2010 Phys. Rev. A 82 044304
[113]	Sheng Y B, Deng F G 2010 Phys. Rev. A 82 044305
[114]	Deng F G 2011 Phys. Rev. A 83 062316
[115]	Sheng Y B, Zhou L 2014 Laser Phys. Lett. 11 085203
[116]	Li X H, Deng F G, Zhou H Y 2007 Appl. Phys. Lett. 91 144101
[117]	Deng F G, Li X H, Zhou H Y 2011 Quant. Inf. Compu. 11 0913
[118]	Kalamidas D 2005 Phys. Lett. A 343 331
[119]	Yamamoto T, Shimamura J, zdemir S K, Koashi M, Imoto N 2005 Phys. Rev. Lett. 95 040503
[120]	Zanardi P, Rasetii M 1997 Phys. Rev. Lett. 79 3306
[121]	Sun Y 2013 Acta Sin. Quantum Opt. 19 122 (in Chinese) [孙越 2013 量子光学学报 19 122]
[122]	Han C, Zhou Z W, Guo G C 2006 J. Phys. B 39 1677
[123]	Yamamoto T, Nagase R, Shimamura J, zdemir S K, Koashi M, Imoto N 2007 New. J. Phys. 9 191
[124]	Yamamoto T, Hayashi K, zdemir S K, Koashi M, Imoto N 2008 Nat. Photon. 2 488
[125]	Ikuta R, Ono Y, Tashima T, Yamamoto T, Koashi M, Imoto N 2011 Phys. Rev. Lett. 106 110503
[126]	Kumagai H, Yamamoto T, Koashi M, Imoto N 2013 Phys. Rev. A 87 052325
[127]	Li X H, Deng F G, Zhou H Y 2009 Opt. Commun. 282 4025
[128]	Dong L, Xiu X M, Gao Y J, Chi F 2010 Commun. Theor. Phys. 54 269
[129]	Dong L, Wang J X, Shen H Z, Li D, Xiu X M, Gao Y J, Yi X X 2014 Quant. Inf. Process. 13 1413
[130]	Gao M, Liang L M, Li C Z, Tian C L 2006 Phys. Lett. A 359 126
[131]	Sheng Y B, Deng F G 2010 Phys. Rev. A 81 042332
[132]	Niu H C, Ren B C, Wang T J, Hua M, Deng F G 2012 Int. J. Theor. Phys. 51 2346
[133]	Li Y, Chen X, Zeng Z, Li X H 2013 Commun. Theor. Phys. 59 32
[134]	Chen X, Li Y, Zeng Z, Li X H 2013 Commun. Theor. Phys. 60 421
[135]	Kang Y H, Xia Y, Lu P M 2014 Appl. Phys. B 116 977
[136]	Zeng Z, Wang C, Li X H, Wei H 2015 Laser Phys. Lett. 12 015201
[137]	Zhang Z J 2006 Physica A 361 233
[138]	Li X H, Deng F G, Zhou H Y 2009 Int. J. Quantum Inf. 7 1479
[139]	Li C Y, Li Y S 2010 Int. J. Quantum Inf. 8 1101
[140]	Xiu X M, Dong L, Gao Y J, Chi F 2009 Opt. Commun. 282 4171
[141]	Lin S, Guo G D, Gao F, Liu X F 2014 Quant. Inf. Comput. 14 0845
[142]	Lai H, Orgun M A, Xiao J H, Xue L Y 2014 Quant. Inf. Process. 13 1523
[143]	Yuan H, Song J, He Q, Han L F, Hou K, Hu X Y, Shi S H 2008 Commun. Theor. Phys. 50 627
[144]	Gu B, Pei S X, Song B, Zhong K 2009 Sci. China: Phys. Mech. Astron. 52 1913
[145]	Dong L, Xiu X M, Gao Y J, Chi F 2009 Opt. Commun. 282 1688
[146]	Dong H K, Dong L, Xiu X M, Gao Y J 2010 Int. J. Quantum Inf. 8 1389
[147]	Yang C W, Tsai C W, Hwang T 2013 Quant. Inf. Process. 12 3043
[148]	Yang C W, Hwang T 2013 Quant. Inf. Process. 12 3495
[149]	Yuan H, Zhang Q, Hong L, Yin W J, Xu D 2014 Int. J. Theor. Phys. 53 2565
[150]	Wang C, Liu J W, Chen X B, Bi Y G, Shang T 2015 Chin. Phys. B 24 040304
[151]	Gu B, Mu L, Ding L, Zhang C, Li C 2010 Opt. Commun. 283 3099
[152]	Li C Y, Li Y S 2011 Chin. Phys. Lett. 28 020304
[153]	Gu B, Zhang C Y, Cheng G S, Huang Y G 2011 Sci. China: Phys. Mech. Astron. 54 942
[154]	Yang C W, Tsai C W, Hwang T 2011 Sci. China: Phys. Mech. Astron. 54 496
[155]	Yang C W, Hwang T 2012 Int. J. Theor. Phys. 51 3941
[156]	Huang W, Wen Q Y, Jia H Y, Qin S J, Gao F 2012 Chin. Phys. B 21 100308
[157]	Yang C W, Tsai C W, Hwang T 2014 Laser Phys. 24 105203
[158]	Yang C W, Hwang T 2013 Quant. Inf. Process. 12 2131
[159]	Ye T Y 2015 Quant. Inf. Process. 14 1487
[160]	Aolita L, Walborn S P 2007 Phys. Rev. Lett. 98 100501
[161]	Souza C E R, Borges C V S, Khoury A Z 2008 Phys. Rev. A 77 032345
[162]	Yamamoto T, Nagase R, Shimamura J, zdemir S K, Koashi M, Imoto N 2007 New J. Phys. 9 191
[163]	Yamamoto T, Hayashi K, zdemir S K, Koashi M, Imoto N 2008 Nature Photon. 2 488
[164]	Li T, Wang G Y, Deng F G, Long G L 2016 Sci. Rep. 6 20677
[165]	Gao C Y, Wang G Y, Zhang H, Deng F G 2017 Quantum Inf. Process. 16 11
[166]	Jiang Y X, Guo P L, Gao C Y, Wang H B, Alzahrani F, Hobiny A, Deng F G 2017 Sci. China: Phys. Mech. Astron. 60 120312
[167]	Gisin N, Pironio S, Sangouard N 2010 Phys. Rev. Lett. 105 070501
[168]	Bruno N, Pini V, Martin A, Verma V B, Nam S W, Mirin R, Lita A, Marsili F, Krozh B, Bussires F, Sangouard N, Zbinden H, Gisin N, Thew R 2016 Opt. Express 24 125
[169]	Meyer-Scott E, Bula M, Bartkiewicz K, Cernoch A, Soubusta J, Jennewein T, Lemr K 2013 Phys. Rev. A 88 012327
[170]	Zhou L, Sheng Y B 2015 Laser Phys. Lett. 12 045203
[171]	Ouyang Y, Feng Z F, Zhou L, Sheng Y B 2015 Quant. Inf. Process. 14 635
[172]	Ouyang Y, Feng Z F, Zhou L, Sheng Y B 2016 Laser Phys. 26 015204
[173]	Walborn S P, Souto Ribeiro P H, Davidovich L, Mintert F, Buchleitner A 2006 Nature 440 1022
[174]	Lee S M, Ji S W, Lee H W, Zubairy M S 2008 Phys. Rev. A 77 040301
[175]	Zhou L, Sheng Y B 2014 Phys. Rev. A 90 024301
[176]	Sheng Y B, Guo R, Pan J, Zhou L, Wang X F 2015 Quant. Inf. Process. 14 963
[177]	Zhou L, Sheng Y B 2015 Entropy 17 4293
[178]	Zwerger M, Briegel H J, Dr W 2013 Phys. Rev. Lett. 110 260503
[179]	Zwerger M, Briegel H J, Dr W 2014 Phys. Rev. A 90 012314
[180]	Sheng Y B, Zhou L 2016 Sci. Rep. 5 13453
[181]	Zhou L, Sheng Y B 2015 Phys. Rev. A 92 042314
[182]	Lloyd S, Mohseni M, Rebentrost P 2013 arXiv: 1307.0411
[183]	Rebentrost P, Mohseni M, Lloyd S 2014 Phys. Rev. Lett. 113 130503
[184]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025

[1]	Wu Xiao-Dong, Huang Duan. Practical continuous variable quantum secret sharing scheme based on non-ideal quantum state preparation. Acta Physica Sinica, 2024, 73(2): 020304. doi: 10.7498/aps.73.20230138
[2]	Liu Zhao. Fractionalized topological states in moiré superlattices. Acta Physica Sinica, 2024, 73(20): 207303. doi: 10.7498/aps.73.20241029
[3]	Wang Wei, Wang Yi-Ping. Modulation of topological phase transitions and topological quantum states in one-dimensional superconducting transmission line cavities lattice. Acta Physica Sinica, 2022, 71(19): 194203. doi: 10.7498/aps.71.20220675
[4]	Wei Yu-Yan, Gao Zi-Kai, Wang Si-Ying, Zhu Ya-Jing, Li Tao. Deterministic secure quantum communication with double-encoded single photons. Acta Physica Sinica, 2022, 71(5): 050302. doi: 10.7498/aps.71.20210907
[5]	. Deterministic secure quantum communication with double-encoded single photons. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20210907
[6]	Ding Chen, Li Tan, Zhang Shuo, Guo Chu, Huang He-Liang, Bao Wan-Su. A quantum state readout method based on a single ancilla qubit. Acta Physica Sinica, 2021, 70(21): 210303. doi: 10.7498/aps.70.20211066
[7]	Yang Le, Li Kai, Dai Hong-Yi, Zhang Ming. A novel scheme of quantum state tomography based on quantum algorithms. Acta Physica Sinica, 2019, 68(14): 140301. doi: 10.7498/aps.68.20190157
[8]	Zhang Yao, Zhang Yang, Dong Zhen-Chao. Single-molecule electroluminescence and its relevant latest progress. Acta Physica Sinica, 2018, 67(22): 223301. doi: 10.7498/aps.67.20181718
[9]	Li Xi-Han. Quantum secure direct communication. Acta Physica Sinica, 2015, 64(16): 160307. doi: 10.7498/aps.64.160307
[10]	Ma Hong-Yang, Qin Guo-Qing, Fan Xing-Kui, Chu Peng-Cheng. Quantum network direct communication protocol over noisy channel. Acta Physica Sinica, 2015, 64(16): 160306. doi: 10.7498/aps.64.160306
[11]	Chen Jun, Yu Ya-Fei, Zhang Zhi-Ming. Optimizing quantum state transfer in multi-excitation spin chains via information flux. Acta Physica Sinica, 2015, 64(16): 160305. doi: 10.7498/aps.64.160305
[12]	Wu Shi-Hai, Hu Ming-Liang, Li Ji, Xi Xiao-Qiang. Using Josephson charge qubits system to realize the transfer of a special kind of quantum state. Acta Physica Sinica, 2011, 60(1): 010302. doi: 10.7498/aps.60.010302
[13]	Li Yong-Fang, Ren Li-Qing, Ma Rui-Qiong, Fan Rong, Liu Juan. Implementing quantum control for the temporal evolution of the wave function of the quantum state by using a phase-controlled light field. Acta Physica Sinica, 2010, 59(3): 1671-1676. doi: 10.7498/aps.59.1671
[14]	Hu Ju-Ju, Cai Shi-Hua, Wang Jian-Qiu, Ji Ying-Hua. Study on the influence of quantum state for phonon bath on the quantum behavior of mesoscopic circuit. Acta Physica Sinica, 2008, 57(1): 496-501. doi: 10.7498/aps.57.496
[15]	Ma Rui-Qiong, Li Yong-Fang, Shi Jian. Measurement of quantum states with incoherent light. Acta Physica Sinica, 2008, 57(9): 5593-5599. doi: 10.7498/aps.57.5593
[16]	Zhang Miao, Jia Huan-Yu, Ji Xiao-Hui, Si Kun, Wei Lian-Fu. Generation of squeezed quantum states of a single trapped cold ion. Acta Physica Sinica, 2008, 57(12): 7650-7657. doi: 10.7498/aps.57.7650
[17]	Liu Jing, Sun Jun-Qiang, Huang De-Xiu, Huang Chong-Qing, Wu Ming. Modulated photon confined states with graded-index photonic quantum well structure. Acta Physica Sinica, 2007, 56(4): 2281-2285. doi: 10.7498/aps.56.2281
[18]	Hu Xue-Ning, Li Xin-Qi. Quantum measurement of single electron state by a quantum point contact. Acta Physica Sinica, 2006, 55(7): 3259-3264. doi: 10.7498/aps.55.3259
[19]	Song Tong-Qiang. Teleportation of quantum states by means of two-mode squeezed vacuum. Acta Physica Sinica, 2004, 53(10): 3358-3362. doi: 10.7498/aps.53.3358
[20]	Zhang Quan, Zhang Er-Yang, Tang Chao-Jing. . Acta Physica Sinica, 2002, 51(8): 1675-1683. doi: 10.7498/aps.51.1675

Catalog

Vol. 67, Issue 13 - 2018-07-05

Metrics

Abstract views: 7825
PDF Downloads: 578
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板