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Liao Xiang-Ping et al.(Chin. Phys. B 23 020304, 2014) pointed out that the method of weak measurement and quantum weak measurement reversal can protect entanglement and improve the fidelity of three-qubit quantum state. We generalize the method of weak measurement to the case of qudit state in this paper. By using the operation of weak measurement and quantum weak measurement reversal, we investigate the evolution dynamics of fidelity and fidelity improvement for qudit state under amplitude damping decoherence. We compare two kinds of operations: one is to let the input qudit state cross the amplitude damping decoherence directly, and the other one is that we first make a weak measurement operation on the input qudit state, then through the amplitude damping decoherence, finally an operation of quantum weak measurement reversal is done with the output qudit state. We discuss the GHZ state, W state, CL state and some special separable states exactly and obtain the analytic expressions of fidelity and fidelity improvement for qudit state before and after the weak measurement and quantum weak measurement reversal operation. According to the analytic expressions we plot the evolution curves against its corresponding parameters. The effects of corresponding parameters are discussed and a susceptible protection region of the qudit state is also given in the context. The results show that the structure of qudit state is the determined factor to the effect of weak measurement and quantum weak measurement reversal. There are some different effects on the different structured qudit states. For entangled state, the fidelity of qudit GHZ state can be protected in a relatively big evolution region, most part of the fidelity improvement is in the upper part of the zero reference plane. While the fidelity of qudit W state can be improved effectively in the whole evolution region, which is a perfect protection. The evolution regulations of qudit CL state and Dick state are between evolution regulations of the GHZ state and W state. When we input some special separable qudit states which have similar structures to W state, their fidelity and fidelity improvement are almost the same as W state’s. It is demonstrated that the structure of qudit state is important for the weak measurement in a step. This work is meaningful for the quantum information process.
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Keywords:
- weak measurement /
- qudit /
- amplitude /
- fidelity
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[2] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[3] Nielsen M A, Chuang I L 2002 Quantum Computation and Quantum Informatin（Cambridge:Cambridge University Press) pp74-89
[4] Zeng H F, Shao B, Yang L G, Li J, Zou J 2008 Chin. Phys. B 18 3265
[5] Sun G H, Aoki M A, Dong S H 2013 Chin. Phys. B 22 050302
[6] Yu T, Eberly J H 2007 arXiv preprint arXiv:0707.3215
[7] Zhang R, Qin H, Tang B, Xue P 2013 Chin. Phys. B 22 100301
[8] Mazhar A, Alber G, Rau A R P 2009 J. Phys. B 42 025501
[9] Mazhar A, Guhne O 2014 J. Phys. B 47 055503
[10] Yu T, Eberly J H 2003 Phys. Rev. Lett. 97 140403
[11] Simon C, Kempe J 2002 Phys. Rev. A 65 052327
[12] López C E, Römero G, Lastra F, Solano E, Reamal J C 2008 Phys. Rev. Lett. 101 080503
[13] Yu T, Eberly J H 2002 Phys. Rev. B 66 193306
[14] Yu T, Eberly J H 2003 Phys. Rev. B 68 165322
[15] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[16] Yang B Y, Fang M F, Huang J 2013 Chin. Phys. B 22 080303
[17] Pan J W, Gasparoni S, Ursin R, Weihs G, Zeilinger A 2003 Nature Phys. 423 1014
[18] Xiao X, Fang M F, Li Y L, Zeng K, Wu C 2009 J. Phys. B:At. Mol. Opt. Phys. 42 235502
[19] Huang J, Guo Y N, Xie Q 2016 Chin. Phys. B 25 0203032
[20] Zou H M, Fang M F 2016 Chin. Phys. B 25 090302
[21] Fan Z L, Ren Y K, Zeng H S 2016 Chin. Phys. B 25 010303
[22] Han W, Jiang K X, Zhang Y J, Xia Y J 2015 Chin. Phys. B 24 120304
[23] Mazhar A 2015 Chin. Phys. B 24 1203035
[24] Mazhar A, Huang J 2014 Chin. Phys. Lett. 31 110301
[25] Wang Z L, Wang Z, Fan H Y 2015 Chin. Phys. B 24 1203016
[26] Yang Y B, Wang W G 2015 Chin. Phys. Lett. 32 030301
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[28] Zou Q, Hu X M, Liu J M 2015 Acta Phys. Sin. 64 080302 （in Chinese)[邹琴, 胡小勉, 刘金明2015物理学报64 080302]
[29] Korotkov A N 1999 Phys. Rev. B 60 5737
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[31] Korotkov A N, Jordan A N 2006 Phys. Rev. Lett. 97 166805
[32] Kim Y S, Cho Y W, Ra Y S, Kim Y H 2009 Opt. Express 17 11978
[33] Lee J C, Jeong Y C, Kim Y S, Kim Y H 2011 Opt. Express 19 16309
[34] Xu X Y, Kedem Y, Sun K, Vaidman L, Li C F, Guo G C 2013 Phys. Rev. Lett. 111 033604
[35] Katz N, Ansmann M, Bialczak R C, Lucero E, Mcdermott R, Neeley M, Steffen M, Weig E M, Cleland A N, Martinis J M, Korotkov A N 2006 Science 312 1498
[36] Groen J P, Riste D, Tornberg L, CRömer J, Degroot P C, Picot T, Johansson G, Dicarlo L 2013 Phys. Rev. Lett. 111 090506
[37] Korotkov A N, Keane K 2010 Phys. Rev. A 81 040103
[38] Wang S C, Yu Z W, Wang X B 2014 Phys. Rev. A 89 022318
[39] Sun Q Q, Amri M A, Zubairy M S 2009 Phys. Rev. A 80 033838
[40] Kim Y S, Lee J C, Kwon O, Kim Y H 2012 Nature Phys. 8 117
[41] Xiao X, Li Y L 2013 Eur. Phys. J. D 67 204
[42] Liao X P, Fang M F, Fang J S, Zhu Q Q 2014 Chin. Phys. B 23 020304
[43] Schumacher B W 1996 Phys. Rev. A 54 2614
[44] Song X L, Yang M 2016 Acta Phys. Sin. 65 080303 （in Chinese)[宗晓岚, 杨名2016物理学报65 080303]
[45] Xiao X, Feng M 2011 Phys. Rev. A 83 054301
[46] Jungnitsch B, Moroder T, Guhne O 2011 Phys. Rev. Lett. 106 190502
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[1] Zhou S X 2002 Quantum Dynamics（Beijing:Higher Education Press) pp17-25(in Chinese)[周世勋2002量子力学(北京:高等教育出版社)第17–25页]
[2] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[3] Nielsen M A, Chuang I L 2002 Quantum Computation and Quantum Informatin（Cambridge:Cambridge University Press) pp74-89
[4] Zeng H F, Shao B, Yang L G, Li J, Zou J 2008 Chin. Phys. B 18 3265
[5] Sun G H, Aoki M A, Dong S H 2013 Chin. Phys. B 22 050302
[6] Yu T, Eberly J H 2007 arXiv preprint arXiv:0707.3215
[7] Zhang R, Qin H, Tang B, Xue P 2013 Chin. Phys. B 22 100301
[8] Mazhar A, Alber G, Rau A R P 2009 J. Phys. B 42 025501
[9] Mazhar A, Guhne O 2014 J. Phys. B 47 055503
[10] Yu T, Eberly J H 2003 Phys. Rev. Lett. 97 140403
[11] Simon C, Kempe J 2002 Phys. Rev. A 65 052327
[12] López C E, Römero G, Lastra F, Solano E, Reamal J C 2008 Phys. Rev. Lett. 101 080503
[13] Yu T, Eberly J H 2002 Phys. Rev. B 66 193306
[14] Yu T, Eberly J H 2003 Phys. Rev. B 68 165322
[15] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[16] Yang B Y, Fang M F, Huang J 2013 Chin. Phys. B 22 080303
[17] Pan J W, Gasparoni S, Ursin R, Weihs G, Zeilinger A 2003 Nature Phys. 423 1014
[18] Xiao X, Fang M F, Li Y L, Zeng K, Wu C 2009 J. Phys. B:At. Mol. Opt. Phys. 42 235502
[19] Huang J, Guo Y N, Xie Q 2016 Chin. Phys. B 25 0203032
[20] Zou H M, Fang M F 2016 Chin. Phys. B 25 090302
[21] Fan Z L, Ren Y K, Zeng H S 2016 Chin. Phys. B 25 010303
[22] Han W, Jiang K X, Zhang Y J, Xia Y J 2015 Chin. Phys. B 24 120304
[23] Mazhar A 2015 Chin. Phys. B 24 1203035
[24] Mazhar A, Huang J 2014 Chin. Phys. Lett. 31 110301
[25] Wang Z L, Wang Z, Fan H Y 2015 Chin. Phys. B 24 1203016
[26] Yang Y B, Wang W G 2015 Chin. Phys. Lett. 32 030301
[27] Shan C J, Xia Y J 2006 Acta Phys. Sin. 55 1585 （in Chinese)[单传家, 夏云杰2006物理学报55 1585]
[28] Zou Q, Hu X M, Liu J M 2015 Acta Phys. Sin. 64 080302 （in Chinese)[邹琴, 胡小勉, 刘金明2015物理学报64 080302]
[29] Korotkov A N 1999 Phys. Rev. B 60 5737
[30] Katz N, Neeley M, Ansmann M, Radoslaw C B, Hofheinz M, Lucero E, Connell A, Wang H, Cleland A N, Martinis J M, Korotkov A N 2008 Phys. Rev. Lett. 101 200401
[31] Korotkov A N, Jordan A N 2006 Phys. Rev. Lett. 97 166805
[32] Kim Y S, Cho Y W, Ra Y S, Kim Y H 2009 Opt. Express 17 11978
[33] Lee J C, Jeong Y C, Kim Y S, Kim Y H 2011 Opt. Express 19 16309
[34] Xu X Y, Kedem Y, Sun K, Vaidman L, Li C F, Guo G C 2013 Phys. Rev. Lett. 111 033604
[35] Katz N, Ansmann M, Bialczak R C, Lucero E, Mcdermott R, Neeley M, Steffen M, Weig E M, Cleland A N, Martinis J M, Korotkov A N 2006 Science 312 1498
[36] Groen J P, Riste D, Tornberg L, CRömer J, Degroot P C, Picot T, Johansson G, Dicarlo L 2013 Phys. Rev. Lett. 111 090506
[37] Korotkov A N, Keane K 2010 Phys. Rev. A 81 040103
[38] Wang S C, Yu Z W, Wang X B 2014 Phys. Rev. A 89 022318
[39] Sun Q Q, Amri M A, Zubairy M S 2009 Phys. Rev. A 80 033838
[40] Kim Y S, Lee J C, Kwon O, Kim Y H 2012 Nature Phys. 8 117
[41] Xiao X, Li Y L 2013 Eur. Phys. J. D 67 204
[42] Liao X P, Fang M F, Fang J S, Zhu Q Q 2014 Chin. Phys. B 23 020304
[43] Schumacher B W 1996 Phys. Rev. A 54 2614
[44] Song X L, Yang M 2016 Acta Phys. Sin. 65 080303 （in Chinese)[宗晓岚, 杨名2016物理学报65 080303]
[45] Xiao X, Feng M 2011 Phys. Rev. A 83 054301
[46] Jungnitsch B, Moroder T, Guhne O 2011 Phys. Rev. Lett. 106 190502
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