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The purpose of quantum teleportation is to achieve perfect transmission of quantum information from one site to another distant site. In the teleportation process, the quantum system is inevitably affected by its surrounding environment, causing the system to lose its coherence, which will result in distortion of the transmitted information. In recent years, weak measurement and measurement reversal have been proposed to suppress the decoherence of quantum entanglement and protect some quantum states. On the other hand, quantum Fisher information (QFI) is an important physical quantity in quantum metrology, which can give the optimal value estimating the accuracy of parameters. As is well known, QFI is highly susceptible to environmental noise and can lead its measurement accuracy to decrease. Therefore, it is of great importance to examine how to protect QFI from being influenced by the external circumstance during the teleportation procedure. In this paper, we study how to improve the QFI of teleporting a single-qubit state via a Greenberger-Horne-Zeilinger state in a finite temperature environment with the technique of weak measurement and weak measurement reversal. According to different qubit transmission cases of three quantum teleportation schemes, we consider their respective QFIs in detail. After constructing the quantum logic circuit of each teleportation scheme, we first analyze the variance trend of QFI against the generalized amplitude damping noise parameters. Then by introducing weak measurement and measurement reversal on each noise particle of the three schemes, we optimize the related partial measurement parameters and explore the corresponding improved QFI, namely, the difference between the QFI with optimal partial measurements and that without partial measurements. We find that optimizing partial measurements can efficiently enhance the QFI of the teleported state for the three kinds of teleportation schemes at finite temperature. Moreover, with the value of p fixed, the lower the environment temperature, the larger the value of the improved QFI is. Our results could be useful in further understanding the applications of weak measurement and measurement reversal to the quantum communication process and may shed light on estimating some relevant quantum parameters and implementing quantum information tasks.
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Keywords:
- quantum teleportation /
- generalized amplitude damping /
- weak measurement /
- quantum Fisher information
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[1] Yin J, Cao Y, Li Y H, et al. 2017 Science 356 1140
[2] Liao S K, Cai W Q, Handsteiner J, et al. 2018 Phys. Rev. Lett. 120 030501
[3] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[4] Gottesman D, Chuang I L 1999 Nature 402 390
[5] Yang L, Ma H Y, Zheng C, Ding X L, Gao J C, Long G L 2017 Acta Phys. Sin. 66 230303 (in Chinese) [杨璐, 马鸿洋, 郑超, 丁晓兰, 高健存, 龙桂鲁 2017 物理学报 66 230303]
[6] Braunstein S L, Kimble H J 1998 Phys. Rev. Lett. 80 869
[7] Yonezawa H, Aoki T, Furusawa A 2004 Nature 431 430
[8] Zhang J, Peng K C 2000 Phys. Rev. A 62 064302
[9] Dell'Anno F, de Siena S, Illuminati F 2010 Phys. Rev. A 81 012333
[10] Hillery M, Buzek V, Berthiaume A 1999 Phys. Rev. A 59 1829
[11] Bell B A, Markham D, Herrera-Marti D A, Marin A, Wadsworth W J, Rarity J G, Tame M S 2014 Nat. Commun. 5 5480
[12] Kogias I, Xiang Y, He Q Y, Adesso G 2017 Phys. Rev. A 95 012315
[13] Deng F G, Li C Y, Li Y S, Zhou H Y, Wang Y 2005 Phys. Rev. A 72 022338
[14] Zhou P, Li X H, Deng F G, Zhou H Y 2007 J. Phys. A: Math. Theor. 40 13121
[15] Man Z X, Xia Y J, An N B 2007 Phys. Rev. A 75 052306
[16] Huelga S F, Plenio M B, Vaccaro J A 2002 Phys. Rev. A 65 042316
[17] Han X P, Liu J M 2008 Phys. Scr. 78 015001
[18] Li W L, Li C F, Guo G C 2000 Phys. Rev. A 61 034301
[19] Pati A K, Agrawal P 2007 Phys. Lett. A 371 185
[20] Chen X B, Du J Z, Wen Q Y, Zhu F C 2008 Chin. Phys. B 17 771
[21] Yan F L, Yan T 2010 Chin. Sci. Bull. 55 902
[22] Zha X W, Zou Z C, Qi J X, Song H Y 2013 Int. J. Theor. Phys. 52 1740
[23] Li Y H, Nie L P 2013 Int. J. Theor. Phys. 52 1630
[24] Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575
[25] Ren J G, Xu P, Yong H L, et al. 2017 Nature 549 70
[26] Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439
[27] Zhong W, Sun Z, Ma J, Wang X, Nori F 2013 Phys. Rev. A 87 022337
[28] Giovaneti V, Lloyd S, Maccone L 2004 Science 306 1330
[29] Aharonov Y, Albert D Z, Vaidman L 1988 Phys. Rev. Lett. 60 1351
[30] Paraoanu G S 2011 EPL 93 64002
[31] Korotkov A N, Keane K 2010 Phys. Rev. A 81 040103
[32] Branczyk A M, Mendonca P E M F, Gilchrist A, Doherty A C, Bartlett S D 2007 Phys. Rev. A 75 012329
[33] Sun Q Q, Amri M A, Zubairy M S 2009 Phys. Rev. A 80 033838
[34] Song W, Yang M, Cao Z L 2014 Phys. Rev. A 89 014303
[35] Man Z X, Xia Y J, An N B 2012 Phys. Rev. A 86 012325
[36] Liao X P, Fang M F, Fang J S, Zhu Q Q 2014 Chin. Phys. B 23 020304
[37] Xiao X 2014 Phys. Scr. 89 065102
[38] Wang S C, Yu Z W, Zou W J, Wang X B 2014 Phys. Rev. A 89 022318
[39] Huang J 2017 Acta Phys. Sin. 66 010301 (in Chinese) [黄江 2017 物理学报 66 010301]
[40] Guo J L, Wei J L 2015 Ann. Phys. 354 522
[41] Shi J D, Wang D, Ma W C, Ye L 2015 Quantum Inf. Process. 14 3569
[42] Yang R Y, Liu J M 2017 Quantum. Inf. Process. 16 125
[43] Kim Y S, Lee J C, Kwon O, Kim Y H 2012 Nat. Phys. 8 117
[44] Xu X Y, Kedem Y, Sun K, Vaidman L, Li C F, Guo G C 2013 Phys. Rev. Lett. 111 033604
[45] Katz N, Neeley M, Ansmann M, Bialczak R C, Hofheinz M, Lucero E, O'Connell A, Wang H, Cleland A N, Martinis J M, Korotkov A N 2008 Phys. Rev. Lett. 101 200401
[46] Groen J P, Riste D, Tornberg L, Cramer J, Degroot P C, Picot T, Johansson G, Dicarlo L 2013 Phys. Rev. Lett. 111 090506
[47] Pramanik T, Majumdar A S 2013 Phys. Lett. A 377 3209
[48] Qiu L, Tang G, Yang X Q, Wang A M 2014 Ann. Phys. 350 137
[49] Xiao X, Yao Y, Zhong W J, Li Y L, Xie Y M 2016 Phys. Rev. A 93 012307
[50] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) p380
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