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无指针δ-淬火直接测量法测量量子密度矩阵

温永立 张善超 颜辉 朱诗亮

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无指针δ-淬火直接测量法测量量子密度矩阵

温永立, 张善超, 颜辉, 朱诗亮

Scheme of directly measuring quantum density matrix by δ-quench method

Wen Yong-Li, Zhang Shan-Chao, Yan Hui, Zhu Shi-Liang
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  • 量子密度矩阵描述了量子态的性质, 因此如何有效地测量密度矩阵是量子力学的核心课题之一. 最近, 几个研究组发展了一种基于弱值的直接测量密度矩阵的方法. 相较于常用的量子态层析技术, 这种方法能够更直接和更简便地重构密度矩阵. 然而这种方法需要耦合额外的测量指针, 从而也增加了测量的复杂度和测量系统的设计困难. 本文先回顾并讨论了量子态直接测量的相关研究, 然后基于δ-淬火直接测量波函数的方法提出了一种新的直接测量密度矩阵的方法. 这种方法无需耦合外部测量指针, 因此可以降低测量的复杂度和测量系统的设计困难, 更进一步地简化了直接测量密度矩阵的实验过程. 基于此方法, 提出了更高信号强度以及更少操作次数等两种无指针直接测量方案, 并对比分析了它们在不同的测量条件下的优缺点. 最后, 具体设计了测量光子密度矩阵的实验.
    Density matrix, which characterizes a quantum state, plays an important role in quantum mechanics. Recently, a method which can directly measure the elements of a density matrix was proposed. Compared with the conventional quantum state tomography which is widely used to reconstruct the density matrix, this measurement method has the advantages of directness and simplicity. However, this direct measurement method relies on an extra pointer space. The addition of this extra pointer can increase the complexity of an experiment. In this paper, we first review previous work on direct measurement, then we propose a scheme to directly measure the density matrix based on δ-quench, which is also a direct measurement method but needs no additional pointer. This proposal reduces the complexity of the measuring system and further simplifies the measurement. We propose two schemes to realize this δ-quench measurement, then analyse their superiorities in different situations of measurement. An experiment to measure photon's density matrix is also designed.
      通信作者: 朱诗亮, slzhu@scnu.edu.cn
    • 基金项目: 广东省重点领域研发计划(批准号: 2019B030330001)、广州市科技计划重点项目(批准号: 201804020055, 2019050001)、国家重点研发计划(批准号: 2016YFA0301803)和国家自然科学基金(批准号: 12074180) 资助的课题
      Corresponding author: Zhu Shi-Liang, slzhu@scnu.edu.cn
    • Funds: Project supported by the Key-Area Research and Development Program of Guangdong Province, China (Grant No. 2019B030330001), the Key Project of Science and Technology of Guangzhou, China (Grant Nos. 201804020055, 2019050001), the National Key R&D Program of China (Grant No. 2016YFA0301803), and the National Natural Science Foundation of China (Grant No. 12074180)
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    Malik M, Mirhosseini M, Lavery M P J, Leach J, Padgett M J, Boyd R W 2014 Nat. Commun. 5 3115Google Scholar

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    Kocsis S, Braverman B, Ravets S, Stevens M J, Mirin R P, Shalm L K, Steinberg A M 2011 Science 332 1170Google Scholar

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    Lundeen J S, Bamber C 2012 Phys. Rev. Lett. 108 070402Google Scholar

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    Boldu E, Gariepy G, Leach J 2016 Nat. Commun. 7 10439Google Scholar

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    Qin L, Xu L, Feng W, Li X Q 2017 New J. Phys. 19 033036Google Scholar

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    Bamber C, Lundeen J S 2014 Phys. Rev. Lett. 112 070405Google Scholar

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    Shojaee E, Jackson C S, Riofrío C A, Kalev A, Deutsch I H 2018 Phys. Rev. Lett. 121 130404Google Scholar

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    Fischbach J, Freyberger M 2012 Phys. Rev. A 86 052110Google Scholar

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    Mirhosseini M, Magana-Loaiza O S, Rafsanjani S M H, Boyd R W 2014 Phys. Rev. Lett. 113 090402Google Scholar

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    Vallone G, Dequal D 2016 Phys. Rev. Lett. 116 040502Google Scholar

    [25]

    Denkmayr T, Geppert H, Lemmel H, Waegell M, Dressel J, Hasegawa Y, Sponar S 2018 Phys. Rev. Lett. 118 010402

    [26]

    Zhang C R, Hu M J, Xiang G Y, Zhang Y S, Li C F, Guo G C 2020 Chin. Phys. Lett. 37 080301Google Scholar

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    Zhang C R, Hu M J, Hou Z B, Tang J F, Zhu J, Xiang G Y, Li C F, Guo G C, Zhang Y S 2020 Phys. Rev. A 101 012119Google Scholar

    [28]

    Pan W W, Xu X Y, Kedem Y, Wang Q Q, Chen Z, Jan M, Su K, Xu J S, Han Y J, Li C F, Guo G C 2019 Phys. Rev. Lett. 123 150402Google Scholar

    [29]

    Thekkadath G S, Giner L, Chalich Y, Horton M J, Banker J, Lundeen J S 2016 Phys. Rev. Lett. 117 120401Google Scholar

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    Calderaro L, Foletto G, Dequal D, Villoresi P, Vallone G 2018 Phys. Rev. Lett. 121 230501Google Scholar

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    Zhang S, Zhou Y, Mei Y, Liao K, Wen Y L, Li J, Zhang X D, Du S, Yan H, Zhu S L 2019 Phys. Rev. Lett. 123 190402Google Scholar

  • 图 1  (a) 文献[30]中有指针直接测量密度矩阵的方法; (b) 本文提出的无指针直接测量密度矩阵的方法

    Fig. 1.  (a) Schematic of direct measurement method of the density matrix with pointer in Ref. [30]; (b) our proposal of direct measurement method of the density matrix without pointer.

    图 2  (a) 文献[30]提出的有指针直接测量密度矩阵的实验方案; (b) 本文提出的无指针直接测量密度矩阵实验方案

    Fig. 2.  (a) Schematic of direct measurement of the density matrix with pointer in Ref. [30]; (b) experimental proposal of our direct measurement without pointer.

  • [1]

    James D F V, Kwiat P G, Munro W J, White A G 2001 Phys. Rev. A 64 052312Google Scholar

    [2]

    Schmied R 2016 J. Mod. Opt. 63 1744Google Scholar

    [3]

    Lorenzo A D 2013 Phys. Rev. Lett. 110 010404Google Scholar

    [4]

    Lorenzo A D 2013 Phys. Rev. A 88 042114Google Scholar

    [5]

    Bent N, Qassim H, Tahir A A, Sych D, Leuchs G, Sánchez-Soto L L, Karimi E, Boyd R W 2015 Phys. Rev. X 5 041006

    [6]

    Lundeen J S, Sutherland B, Patel A, Stewart C, Bamber C 2011 Nature 474 188Google Scholar

    [7]

    Aharonov Y, Albert D Z, Vaidman L 1988 Phys. Rev. Lett. 60 1351Google Scholar

    [8]

    Dressel J, Malik M, Miatto F M, Jordan A N, Boyd R W 2014 Rev. Mod. Phys. 86 307Google Scholar

    [9]

    Ritchie N W M, Story J G, Hulet R G 1991 Phys. Rev. Lett. 66 1107Google Scholar

    [10]

    Yang G, Lian B W, Nie M 2016 Chin. Phys. B 25 080310Google Scholar

    [11]

    Liao X P, Fang M F, Fang J S, Zhu Q Q 2013 Chin. Phys. B 23 020304

    [12]

    黄江 2017 物理学报 66 010301Google Scholar

    Huang J 2017 Acta Phys. Sin. 66 010301Google Scholar

    [13]

    王美姣, 夏云杰 2015 物理学报 64 240303Google Scholar

    Wang M J, Xia Y J 2015 Acta Phys. Sin. 64 240303Google Scholar

    [14]

    Salvail J Z, Agnew M, Johnson A S, Bolduc E 2013 Nat. Photonics 7 316Google Scholar

    [15]

    Malik M, Mirhosseini M, Lavery M P J, Leach J, Padgett M J, Boyd R W 2014 Nat. Commun. 5 3115Google Scholar

    [16]

    Kocsis S, Braverman B, Ravets S, Stevens M J, Mirin R P, Shalm L K, Steinberg A M 2011 Science 332 1170Google Scholar

    [17]

    Lundeen J S, Bamber C 2012 Phys. Rev. Lett. 108 070402Google Scholar

    [18]

    Boldu E, Gariepy G, Leach J 2016 Nat. Commun. 7 10439Google Scholar

    [19]

    Qin L, Xu L, Feng W, Li X Q 2017 New J. Phys. 19 033036Google Scholar

    [20]

    Bamber C, Lundeen J S 2014 Phys. Rev. Lett. 112 070405Google Scholar

    [21]

    Shojaee E, Jackson C S, Riofrío C A, Kalev A, Deutsch I H 2018 Phys. Rev. Lett. 121 130404Google Scholar

    [22]

    Fischbach J, Freyberger M 2012 Phys. Rev. A 86 052110Google Scholar

    [23]

    Mirhosseini M, Magana-Loaiza O S, Rafsanjani S M H, Boyd R W 2014 Phys. Rev. Lett. 113 090402Google Scholar

    [24]

    Vallone G, Dequal D 2016 Phys. Rev. Lett. 116 040502Google Scholar

    [25]

    Denkmayr T, Geppert H, Lemmel H, Waegell M, Dressel J, Hasegawa Y, Sponar S 2018 Phys. Rev. Lett. 118 010402

    [26]

    Zhang C R, Hu M J, Xiang G Y, Zhang Y S, Li C F, Guo G C 2020 Chin. Phys. Lett. 37 080301Google Scholar

    [27]

    Zhang C R, Hu M J, Hou Z B, Tang J F, Zhu J, Xiang G Y, Li C F, Guo G C, Zhang Y S 2020 Phys. Rev. A 101 012119Google Scholar

    [28]

    Pan W W, Xu X Y, Kedem Y, Wang Q Q, Chen Z, Jan M, Su K, Xu J S, Han Y J, Li C F, Guo G C 2019 Phys. Rev. Lett. 123 150402Google Scholar

    [29]

    Thekkadath G S, Giner L, Chalich Y, Horton M J, Banker J, Lundeen J S 2016 Phys. Rev. Lett. 117 120401Google Scholar

    [30]

    Calderaro L, Foletto G, Dequal D, Villoresi P, Vallone G 2018 Phys. Rev. Lett. 121 230501Google Scholar

    [31]

    Zhang S, Zhou Y, Mei Y, Liao K, Wen Y L, Li J, Zhang X D, Du S, Yan H, Zhu S L 2019 Phys. Rev. Lett. 123 190402Google Scholar

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出版历程
  • 收稿日期:  2021-02-05
  • 修回日期:  2021-03-06
  • 上网日期:  2021-05-22
  • 刊出日期:  2021-06-05

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