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量子度量学是研究量子测量与统计推断的一门学科，主要利用量子手段来提高参数估计的精度，在量子信息处理与测量中起到关键作用.量子参数估计的一般过程包含四个步骤：探针态的制备、参数化过程、对参数化后的输出态进行测量以及根据测量结果估计待测参数.其中探针态的选取对测量精度起着至关重要的作用.然而在实际的量子探针态的制备过程中，初始探针态会受到环境噪声的影响.目前人们已经研究了W态与Greenberger-Horne-Zeilinger（GHZ）态的量子Fisher信息（QFI）在典型噪声通道下的变化行为.由于W态与GHZ态有着不同的纠缠性质，对于W态与GHZ态的叠加态的QFI动力学研究具有重要的实际意义.故此，本文主要研究典型噪声通道对这两种状态的叠加态的QFI动力学行为的影响，得出了QFI随噪声参数的变化行为.结果表明，叠加态中W态组分可明显对抗相位阻尼噪声对探针态的QFI的影响，而其中的GHZ态组分可明显对抗振幅阻尼噪声的影响，从而为在实际环境中选取高精度的参数估计过程提供参考.Quantum metrology is a subject of studying quantum measurement and quantum statistical deduction, and the precision of parameter estimation can be enhanced by quantum properties. In general, the process of parameter estimation includes four steps:preparation of probe state, parameterization process, measurement, and data processing. Of these four steps, the preparation of probe state is the most crucial. However, in practical applications, in the process of preparing quantum probe state, the probe system will couple to its environment, which will inevitably cause the quantum properties of the probe system to deteriorate, and thus reducing the precision of quantum parameter estimation. The dynamics of quantum Fisher information (QFI) for W state and Greenberger-Horne-Zeilinger (GHZ) state have been studied in decoherence channels. Because W state and GHZ state have different entanglement properties, the studies of the dynamics of QFI for the superposition of W state and GHZ state are of practical significance in quantum metrology field. In this paper, the dynamics of QFIs for the superposition of W state and GHZ state in three typical decoherence channels (depolarization channel, amplitude damping channel and phase damping channel) are studied. In the four steps of quantum parameter estimation, our major attention is paid to the first step (i.e., the preparation of probe state). For comparison, the QFIs of different probe states are studied, with the other three steps fixed, i.e., all the probe states will undergo the same parameterization, measurement and estimation process. The parameterization process involved here is a quantum spin operation (specified by the spin rotation direction), which is chosen to maximize the QFI of the probe state. The initial probe states under consideration are the superpositions of W state and GHZ state of three-particle and five-particle systems, and the QFI dynamics of those probe states are studied in the three different typical decoherence channels. By using the operator-sum (Kraus) representation of those three typical decoherence channels, the QFI dynamics of the probe state can be analytically derived in three different decoherence channels. The results show that in the depolarization channel, the maximum QFI of the probe state decreases with the decoherence evolving to zero in the end; in the amplitude damping channel, the QFI of the probe state decreases to the minimum with the decoherence evolution and then increases to the shot noise limit; in the phase damping channel, the QFI of the probe state decreases with the evolution of decoherence, but the final stable value is not zero. Further analyses show that W state component of the superposition plays a role in resisting phase damping and the GHZ state component plays a role in resisting amplitude damping. These results can help us to choose the optimal probe state for maximizing the estimation precision in practice.
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Keywords:
- quantum metrology /
- quantum Fisher information /
- decoherence channel /
- W state /
- GHZ state /
- superposition
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[8] Ozaydin F 2014 Phys. Lett. A 378 3161
[9] Ozaydin F, Altintas A A, Bugu S, Yesilyurt C 2014 Acta Phys. Pol. A 125 606
[10] Luati A 2004 Ann. Stat. 32 1770
[11] Jing X X, Liu J, Xiong H N, Wang X G 2015 Phys. Rev. A 92 012312
[12] Pezzé L, Smerzi A 2009 Phys. Rev. Lett. 102 100401
[13] Escher B M, Filho R L D M, Davidovich L 2011 Nat. Phys. 7 406
[14] Demokowicz-Dobrzański R, Kolodyński J, Gutǎ M 2012 Nat. Commun. 3 1063
[15] Roy S M, Braunstein S L 2008 Phys. Rev. Lett. 100 220501
[16] Greenberger D M, Horne M A, Shimony A, Zeilinger A 1990 Am. J. Phys. 58 1131
[17] Dr W, Vidal G, Cirac J I 2000 Phys. Rev. A 62 062314
[18] Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910
[19] Ma J, Huang Y X, Wang X G, Sun C P 2011 Phys. Rev. A 84 022302
[20] Ozaydin F, Altintas A A, Bugu S, Yesilyurt C 2013 Int. J. Theor. Phys. 52 2977
[21] Ozaydin F, Altintas A A, Bugu S, Yesilyurt C 2014 Int. J. Theor. Phys. 53 3219
[22] Yi X J, Huang G Q, Wang J M 2012 Int. J. Theor. Phys. 51 3458
[23] Erol V 2017 Int. J. Theor. Phys. 56 3202
[24] Erol V 2017 arXiv: 1704.07367 (preprints)
[25] Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press) pp56-57
[26] Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland) pp102-104
[27] Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439
[28] Paris M G A 2009 Int. J. Quantum Inf. 07 125
[29] Ma J, Huang Y X, Wang X G, Sun C P 2011 Phys. Rev. A 84 022302
[30] Pang S S, Brun T A 2014 Phys. Rev. A 90 022117
[31] Liu J, Jing X X, Wang X G 2014 Sci. Rep. 5 8565
[32] Wang X, Shi X 2015 Phys. Rev. A 92 042318
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[1] Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439
[2] Jin G R, Kim S W 2007 Phys. Rev. A 76 043621
[3] Hyllus P, Laskowski W, Krischek P, Schwemmer C, Wieczorek W, Weinfurter H, Pezzé L, Smerzi A 2012 Phys. Rev. A 85 022321
[4] Liu W F, Zhang L H, Li C J 2010 Int. J. Theor. Phys. 49 2463
[5] Liu J, Xiong H N, Song F, Wang X G 2014 Physica A 410 167
[6] Yao Y, Xiao X, Ge L, Wang X G, Sun C P 2014 Phys. Rev. A 89 042336
[7] Giovannetti V, Lloyd S, Maccone L 2006 Phys. Rev. Lett. 96 010401
[8] Ozaydin F 2014 Phys. Lett. A 378 3161
[9] Ozaydin F, Altintas A A, Bugu S, Yesilyurt C 2014 Acta Phys. Pol. A 125 606
[10] Luati A 2004 Ann. Stat. 32 1770
[11] Jing X X, Liu J, Xiong H N, Wang X G 2015 Phys. Rev. A 92 012312
[12] Pezzé L, Smerzi A 2009 Phys. Rev. Lett. 102 100401
[13] Escher B M, Filho R L D M, Davidovich L 2011 Nat. Phys. 7 406
[14] Demokowicz-Dobrzański R, Kolodyński J, Gutǎ M 2012 Nat. Commun. 3 1063
[15] Roy S M, Braunstein S L 2008 Phys. Rev. Lett. 100 220501
[16] Greenberger D M, Horne M A, Shimony A, Zeilinger A 1990 Am. J. Phys. 58 1131
[17] Dr W, Vidal G, Cirac J I 2000 Phys. Rev. A 62 062314
[18] Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910
[19] Ma J, Huang Y X, Wang X G, Sun C P 2011 Phys. Rev. A 84 022302
[20] Ozaydin F, Altintas A A, Bugu S, Yesilyurt C 2013 Int. J. Theor. Phys. 52 2977
[21] Ozaydin F, Altintas A A, Bugu S, Yesilyurt C 2014 Int. J. Theor. Phys. 53 3219
[22] Yi X J, Huang G Q, Wang J M 2012 Int. J. Theor. Phys. 51 3458
[23] Erol V 2017 Int. J. Theor. Phys. 56 3202
[24] Erol V 2017 arXiv: 1704.07367 (preprints)
[25] Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press) pp56-57
[26] Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland) pp102-104
[27] Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439
[28] Paris M G A 2009 Int. J. Quantum Inf. 07 125
[29] Ma J, Huang Y X, Wang X G, Sun C P 2011 Phys. Rev. A 84 022302
[30] Pang S S, Brun T A 2014 Phys. Rev. A 90 022117
[31] Liu J, Jing X X, Wang X G 2014 Sci. Rep. 5 8565
[32] Wang X, Shi X 2015 Phys. Rev. A 92 042318
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