Scheme of directly measuring quantum density matrix by <i>δ</i>-quench method

Wen Yong-Li; Zhang Shan-Chao; Yan Hui; Zhu Shi-Liang

doi:10.7498/aps.70.20210269

Abstract

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.

Keywords:

Authors and contacts

1.
National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
2.
Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
3.
Frontier Research Institute for Physics, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China

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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References

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Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

[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
[12]	黄江 2017 物理学报 66 010301 Google Scholar Huang J 2017 Acta Phys. Sin. 66 010301 Google Scholar
[13]	王美姣, 夏云杰 2015 物理学报 64 240303 Google Scholar Wang M J, Xia Y J 2015 Acta Phys. Sin. 64 240303 Google Scholar
[14]	Salvail J Z, Agnew M, Johnson A S, Bolduc E 2013 Nat. Photonics 7 316 Google Scholar
[15]	Malik M, Mirhosseini M, Lavery M P J, Leach J, Padgett M J, Boyd R W 2014 Nat. Commun. 5 3115 Google Scholar
[16]	Kocsis S, Braverman B, Ravets S, Stevens M J, Mirin R P, Shalm L K, Steinberg A M 2011 Science 332 1170 Google Scholar
[17]	Lundeen J S, Bamber C 2012 Phys. Rev. Lett. 108 070402 Google Scholar
[18]	Boldu E, Gariepy G, Leach J 2016 Nat. Commun. 7 10439 Google Scholar
[19]	Qin L, Xu L, Feng W, Li X Q 2017 New J. Phys. 19 033036 Google Scholar
[20]	Bamber C, Lundeen J S 2014 Phys. Rev. Lett. 112 070405 Google Scholar
[21]	Shojaee E, Jackson C S, Riofrío C A, Kalev A, Deutsch I H 2018 Phys. Rev. Lett. 121 130404 Google Scholar
[22]	Fischbach J, Freyberger M 2012 Phys. Rev. A 86 052110 Google Scholar
[23]	Mirhosseini M, Magana-Loaiza O S, Rafsanjani S M H, Boyd R W 2014 Phys. Rev. Lett. 113 090402 Google Scholar
[24]	Vallone G, Dequal D 2016 Phys. Rev. Lett. 116 040502 Google 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 080301 Google 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 012119 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
[29]	Thekkadath G S, Giner L, Chalich Y, Horton M J, Banker J, Lundeen J S 2016 Phys. Rev. Lett. 117 120401 Google Scholar
[30]	Calderaro L, Foletto G, Dequal D, Villoresi P, Vallone G 2018 Phys. Rev. Lett. 121 230501 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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Scheme of directly measuring quantum density matrix by δ-quench method

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Corresponding author: Zhu Shi-Liang, slzhu@scnu.edu.cn

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

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Corresponding author: Zhu Shi-Liang, slzhu@scnu.edu.cn

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