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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.
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Keywords:
- quantum measurement /
- density matrix /
- direct measurement
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[1] James D F V, Kwiat P G, Munro W J, White A G 2001 Phys. Rev. A 64 052312
Google Scholar
[2] Schmied R 2016 J. Mod. Opt. 63 1744
Google Scholar
[3] Lorenzo A D 2013 Phys. Rev. Lett. 110 010404
Google Scholar
[4] Lorenzo A D 2013 Phys. Rev. A 88 042114
Google 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 474 188
Google Scholar
[7] Aharonov Y, Albert D Z, Vaidman L 1988 Phys. Rev. Lett. 60 1351
Google Scholar
[8] Dressel J, Malik M, Miatto F M, Jordan A N, Boyd R W 2014 Rev. Mod. Phys. 86 307
Google Scholar
[9] Ritchie N W M, Story J G, Hulet R G 1991 Phys. Rev. Lett. 66 1107
Google Scholar
[10] Yang G, Lian B W, Nie M 2016 Chin. Phys. B 25 080310
Google Scholar
[11] Liao X P, Fang M F, Fang J S, Zhu Q Q 2013 Chin. Phys. B 23 020304
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Huang J 2017 Acta Phys. Sin. 66 010301
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Google Scholar
Wang M J, Xia Y J 2015 Acta Phys. Sin. 64 240303
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[25] Denkmayr T, Geppert H, Lemmel H, Waegell M, Dressel J, Hasegawa Y, Sponar S 2018 Phys. Rev. Lett. 118 010402
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Google Scholar
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Google 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 150402
Google Scholar
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Google Scholar
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Google 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 190402
Google Scholar
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