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).

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Cited By

[1]	Bennett C H, Brassard G 1984 Proceedings of International Conference on Computers, System and Signal Processing Bangalore, India, IEEE 175
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[4]	Deng F G, Long G L 2003 Phys. Rev. A 68 042315
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[7]	Li X H, Deng F G, Zhou H Y 2008 Phys. Rev. A 78 022321
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[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
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[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
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[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)
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[31]	Wei H R, Deng F G 2013 Opt. Express 21 17671
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[33]	Song X K, Zhang H, Ai Q, Qiu J, Deng F G 2016 New J. Phys. 18 023001
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[35]	Li T, Gao J C, Deng F G, Long G L 2018 Ann. Phys. 391 150
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[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
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[41]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025
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[43]	Hua M, Tao M J, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. (Berlin) 530 1700402
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