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贝叶斯频率估计中频率的先验分布对有色噪声作用的影响

杨棣 王元美 李军刚

贝叶斯频率估计中频率的先验分布对有色噪声作用的影响

杨棣, 王元美, 李军刚
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  • 在贝叶斯参数估计理论框架下,研究了被测参数的先验分布对有色噪声的抑制作用.选择一个受1/fα型谱密度有色噪声影响的自旋1/2量子比特作为量子探测系统来估计一个磁场强度的大小,利用贝叶斯代价函数的动力学演化来评判估计的精度,重点研究先验概率分布对噪声非高斯性的限制作用.研究发现:当先验概率的不确定度比较大时,有色噪声的非高斯性对频率估计精度的影响比较小;当先验概率的不确定度比较小时,有色噪声的非高斯性对频率估计精度的影响比较大.
      通信作者: 李军刚, jungl@bit.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11775019)和北京理工大学基础研究基金资助的课题.
    [1]

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    [2]

    Paris M G A, Řeháček J 2010 Quantum Estimation Theory (Berlin: Springer-Verlag) pp1, 2

    [3]

    Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press) pp231, 252

    [4]

    Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland) p64

    [5]

    Dowling J P 2008 Contemp. Phys. 49 125

    [6]

    Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439

    [7]

    Pairs M G A 2009 Int. J. Quantum Inform. 7 125

    [8]

    Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photon. 5 222

    [9]

    Demkowicz-Dobrzański R, Kołodyński J, Guţǎ M 2012 Nat. Commun. 3 1063

    [10]

    Escher B M, de Matos Filho R L, Davidovich L 2011 Nat. Phys. 7 406

    [11]

    Liu Y C, Xu Z F, Jin G R 2011 Phys. Rev. Lett. 107 013601

    [12]

    Liu G Q, Zhang Y R, Chang Y C, Yue J D, Fan H, Pan X Y 2015 Nat. Commun. 6 6726

    [13]

    Giovannetti V, Lloyd S, Maccone L 2006 Phys. Rev. Lett. 96 010401

    [14]

    Jarzyna M, Demkowicz-Dobrzański R 2015 New J. Phys. 17 013010

    [15]

    Demkowicz-Dobrzański R 2011 Phys. Rev. A 83 061802R

    [16]

    Cramér H 1946 Mathematical Methods of Statistics (Princeton, NJ: Princeton University Press) pp498-500

    [17]

    Lu X M, Sun Z, Wang X G, Luo S L, Oh C H 2013 Phys. Rev. A 87 050302

    [18]

    Li N, Luo S L 2013 Phys. Rev. A 88 014301

    [19]

    Lu X M, Wang X G, Sun C P 2010 Phys. Rev. A 82 042103

    [20]

    Zhang Y M, Li X W, Yang W, Jin G R 2013 Phys. Rev. A 88 043832

    [21]

    Chin A W, Huegla S F, Plenio M B 2012 Phys. Rev. Lett. 109 233601

    [22]

    Monras A, Paris M G A 2007 Phys. Rev. Lett. 98 160401

    [23]

    Li X L, Li J G, Wang Y M 2017 Phys. Lett. A 381 216

    [24]

    Ma J, Huang Y X, Wang X G, Sun C P 2011 Phys. Rev. A 84 022302

    [25]

    Zhong W, Sun Z, Ma J, Wang X G, Nori F 2013 Phys. Rev. A 87 022337

    [26]

    Weiss U 1993 Quantum Dissipative System (Singapore: World Scientific) p5

    [27]

    Yoshihara F, Harrabi K, Niskanen A O, Nakamura A, Tsai J S 2006 Phys. Rev. Lett. 97 167001

    [28]

    Kakuyanagi K, Meno T, Saito S, Nakano H, Semba K, Takayanagi H, Deppe F, Shnirman A 2007 Phys. Rev. Lett. 98 047004

    [29]

    Bergli J, Galperin Y M, Altshuler B L 2009 New J. Phys. 11 025002

    [30]

    Benedetti C, Buscemi F, Bordone P 2013 Phys. Rev. A 87 052328

    [31]

    Benedetti C, Paris M G A, Maniscalco S 2014 Phys. Rev. A 89 012114

    [32]

    Ban M 2016 Quantum Inf. Process. 15 2213

    [33]

    Li J G, Wang Y M, Yang D, Zou J 2017 Phys. Rev. A 96 052130

    [34]

    Wiebe N, Granade C E, Ferrie C, Cory D G 2014 Phys. Rev. Lett. 112 190501

    [35]

    Wang J W, Paesani S, Santagati R, Knauer S, Gentile A A, Wiebe N, Petruzzella M, O’Brien J L, Rarity J G, Laing A, Thompson M G 2017 Nat. Phys. 13 551

    [36]

    Stenberg M P V, Köhn O, Wilhelm F K 2016 Phys. Rev. A 93 012122

  • [1]

    Wiseman H M, Milburn G J 2009 Quantum Measurement and Control (England: Cambridge University Press) pp51, 52

    [2]

    Paris M G A, Řeháček J 2010 Quantum Estimation Theory (Berlin: Springer-Verlag) pp1, 2

    [3]

    Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press) pp231, 252

    [4]

    Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland) p64

    [5]

    Dowling J P 2008 Contemp. Phys. 49 125

    [6]

    Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439

    [7]

    Pairs M G A 2009 Int. J. Quantum Inform. 7 125

    [8]

    Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photon. 5 222

    [9]

    Demkowicz-Dobrzański R, Kołodyński J, Guţǎ M 2012 Nat. Commun. 3 1063

    [10]

    Escher B M, de Matos Filho R L, Davidovich L 2011 Nat. Phys. 7 406

    [11]

    Liu Y C, Xu Z F, Jin G R 2011 Phys. Rev. Lett. 107 013601

    [12]

    Liu G Q, Zhang Y R, Chang Y C, Yue J D, Fan H, Pan X Y 2015 Nat. Commun. 6 6726

    [13]

    Giovannetti V, Lloyd S, Maccone L 2006 Phys. Rev. Lett. 96 010401

    [14]

    Jarzyna M, Demkowicz-Dobrzański R 2015 New J. Phys. 17 013010

    [15]

    Demkowicz-Dobrzański R 2011 Phys. Rev. A 83 061802R

    [16]

    Cramér H 1946 Mathematical Methods of Statistics (Princeton, NJ: Princeton University Press) pp498-500

    [17]

    Lu X M, Sun Z, Wang X G, Luo S L, Oh C H 2013 Phys. Rev. A 87 050302

    [18]

    Li N, Luo S L 2013 Phys. Rev. A 88 014301

    [19]

    Lu X M, Wang X G, Sun C P 2010 Phys. Rev. A 82 042103

    [20]

    Zhang Y M, Li X W, Yang W, Jin G R 2013 Phys. Rev. A 88 043832

    [21]

    Chin A W, Huegla S F, Plenio M B 2012 Phys. Rev. Lett. 109 233601

    [22]

    Monras A, Paris M G A 2007 Phys. Rev. Lett. 98 160401

    [23]

    Li X L, Li J G, Wang Y M 2017 Phys. Lett. A 381 216

    [24]

    Ma J, Huang Y X, Wang X G, Sun C P 2011 Phys. Rev. A 84 022302

    [25]

    Zhong W, Sun Z, Ma J, Wang X G, Nori F 2013 Phys. Rev. A 87 022337

    [26]

    Weiss U 1993 Quantum Dissipative System (Singapore: World Scientific) p5

    [27]

    Yoshihara F, Harrabi K, Niskanen A O, Nakamura A, Tsai J S 2006 Phys. Rev. Lett. 97 167001

    [28]

    Kakuyanagi K, Meno T, Saito S, Nakano H, Semba K, Takayanagi H, Deppe F, Shnirman A 2007 Phys. Rev. Lett. 98 047004

    [29]

    Bergli J, Galperin Y M, Altshuler B L 2009 New J. Phys. 11 025002

    [30]

    Benedetti C, Buscemi F, Bordone P 2013 Phys. Rev. A 87 052328

    [31]

    Benedetti C, Paris M G A, Maniscalco S 2014 Phys. Rev. A 89 012114

    [32]

    Ban M 2016 Quantum Inf. Process. 15 2213

    [33]

    Li J G, Wang Y M, Yang D, Zou J 2017 Phys. Rev. A 96 052130

    [34]

    Wiebe N, Granade C E, Ferrie C, Cory D G 2014 Phys. Rev. Lett. 112 190501

    [35]

    Wang J W, Paesani S, Santagati R, Knauer S, Gentile A A, Wiebe N, Petruzzella M, O’Brien J L, Rarity J G, Laing A, Thompson M G 2017 Nat. Phys. 13 551

    [36]

    Stenberg M P V, Köhn O, Wilhelm F K 2016 Phys. Rev. A 93 012122

  • 引用本文:
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出版历程
  • 收稿日期:  2017-08-28
  • 修回日期:  2017-12-28
  • 刊出日期:  2019-03-20

贝叶斯频率估计中频率的先验分布对有色噪声作用的影响

  • 1. 北京理工大学物理学院, 北京 100081
  • 通信作者: 李军刚, jungl@bit.edu.cn
    基金项目: 

    国家自然科学基金(批准号:11775019)和北京理工大学基础研究基金资助的课题.

摘要: 在贝叶斯参数估计理论框架下,研究了被测参数的先验分布对有色噪声的抑制作用.选择一个受1/fα型谱密度有色噪声影响的自旋1/2量子比特作为量子探测系统来估计一个磁场强度的大小,利用贝叶斯代价函数的动力学演化来评判估计的精度,重点研究先验概率分布对噪声非高斯性的限制作用.研究发现:当先验概率的不确定度比较大时,有色噪声的非高斯性对频率估计精度的影响比较小;当先验概率的不确定度比较小时,有色噪声的非高斯性对频率估计精度的影响比较大.

English Abstract

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