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量子相干性作为量子力学一个最显著的特征, 被认为是量子信息过程中很重要的一种量子资源. 单模压缩态和双模压缩态(Einstein-Podolsky-Rosen纠缠态)均具有量子相干性, 在制备和传输过程中的量子相干性对于实际应用具有重要意义. 利用平衡零拍探测重构量子态的协方差矩阵, 本文定量分析了量子态制备过程中的不完美以及信道传输损耗对单模和双模压缩态量子相干性的影响. 实验证明量子态的压缩和纠缠特性及量子相干性对损耗均是鲁棒的. 特别地, 压缩和纠缠特性会随着量子态制备过程中热光子数的增大而减小, 直至消失, 而当压缩和纠缠均已消失时, 量子相干性依然存在. 实验结果为压缩态、纠缠态光场的量子相干性作为量子资源在量子信息过程中的应用提供了参考.
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关键词:
- 压缩态 /
- Einstein-Podolsky-Rosen纠缠态 /
- 量子态纯度 /
- 量子相干性
As one of the most remarkable features of quantum mechanics, quantum coherence is regarded as an important quantum resource in the quantum information processing. The one-mode squeezed state and the two-mode squeezed state (Einstein-Podolsky-Rosen (EPR) entangled states) as the most representative examples of nonclassical states both have quantum coherence. The squeezing property of the squeezed state is described by the variance of quadrature components, and the positive partial transposition (PPT) criterion is used to describe the entanglement of the EPR entangled states. The research of the quantum coherence of Gaussian states is also a bridge between the properties of squeezing and entanglement. It has been shown that the quantum coherence with infinite-dimensional systems can be quantified by relative entropy. One of the widely used effective methods to obtain the value of quantum coherence experimentally is the quantum tomography. The covariance matrices of the quantum states are reconstructed via balanced homodyne detection and then taken into quantum coherence expression to calculate the corresponding value. The main factors affecting quantum coherence are the classical and uncorrelated noise in the actual experimental generation processing and the decoherence effect caused by the coupling between quantum resources and the surrounding environment. And the quantum coherence evolution in the generation and transmission process of the quantum resources is essential for the practical applications. Therefore, we analyze in detail the influences of the impurity of quantum resource on squeezing, entanglement and quantum coherence. The evolutions of quantum coherence of these Gaussian states in the lossy channels are demonstrated experimentally. The quantum coherence is shown to be robust against the loss in the lossy channels, which is similar to the case of squeezing and entanglement. The quantum coherences of the squeezed states and the EPR entangled states are robust against the thermal photons in the actual experimental generation processing, although the squeezing and entanglement of Gaussian states disappear at a certain number of thermal photons. Our research results provide a reference for the practical applications of quantum coherence of the squeezed state and entangled states in the lossy environment.-
Keywords:
- squeezed state /
- Einstein-Podolsky-Rosen entangled states /
- purity of quantum state /
- quantum coherence
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图 4 双模压缩态实验结果 (a) PPT值随热光子数的变化; (b) 量子相干性随热光子数的变化; (c) 纠缠特性随传输效率的变化; (d) 量子相干性随传输效率的变化
Fig. 4. Experimental results of the two-mode squeezed states in lossy channels: (a) Dependence of PPT value on the number of thermal photons; (b) dependence of quantum coherence on the number of thermal photons; (c) dependence of PPT values on the transmission efficiency; (d) decoherence of quantum coherence in the lossy channels.
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[1] Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401
Google Scholar
[2] Li Y C, Lin H Q 2016 Sci. Rep. 6 26365
Google Scholar
[3] Shi Y H, Shi H L, Wang X H, Hu M L, Liu S Y, Yang W L, Fan H 2020 J. Phys. A 53 085301
Google Scholar
[4] Hillery M 2016 Phys. Rev. A 93 012111
Google Scholar
[5] Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502
Google Scholar
[6] Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145
Google Scholar
[7] Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photonics 5 222
Google Scholar
[8] Giorda P, Allegra M 2016 J Phys. A-Math. Theor. 51 2
Google Scholar
[9] Zhang A, Zhang K, Zhou L, ZhangW 2018 Phys. Rev. Lett. 121 073602
Google Scholar
[10] Yuan Y, Hou Z, Zhao Y Y, Zhong H S, Xiang G Y, Li C F, Guo G C 2018 Opt. Express 26 004470
Google Scholar
[11] Wu K D, Hou Z, Zhong H S, Yuan Y, Guo G C 2017 Optica 4 454
Google Scholar
[12] Zhang M, Kang H J, Wang M H, Xu X L, Peng K C 2021 Photonics Res. 9 887
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[13] Tan K C, Volkoff T, Kwon H, Jeong H 2017 Phys. Rev. Lett. 119 190405
Google Scholar
[14] Tan K C, Jeong H 2018 Phys. Rev. Lett. 121 220401
Google Scholar
[15] Lostaglio M, Müller M P 2019 Phys. Rev. Lett. 123 020403
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Google Scholar
Lin Y, Huang M D, Yu Y F, Zhang Z M 2017 Acta Phys. Sin. 66 110301
Google Scholar
[17] Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439
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[18] Feng X N, Wei L F 2017 Sci. Rep. 7 15492
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[19] Zhang Y R, Shao L H, Li Y, Fan H 2016 Phys. Rev. A 93 012334
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[20] Xu J 2016 Phys. Rev. A 93 032111
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[21] Buono D, Buono G, Petrillo G, Torre G, Zonzo G, Illuminati F 2016 arXiv: 1609.00913
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Zhou Y Y, Liu Y H 2021 Acta Phys. Sin. 70 104203
Google Scholar
[23] Yan Z H, Qin J, Qin Z Z, Su X L, Jia X J, Xie C D, Peng K C 2021 Fundamental Research 1 43
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[24] Chou C W, Hume D B, Thorpe M J, Wineland D J, Rosenband T 2011 Phys. Rev. Lett. 106 160801
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[26] Liu S S, Lou Y B, Chen Y X, Jing J T 2022 Phys. Rev. Lett. 128 060503
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Google Scholar
[33] Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nat. Phys. 4 472
Google Scholar
[34] Guo X S, Breum C R, Borregaard J, Izumi S, Larsen M V, Gehring T, Christandl M, Neergaard-Nielsen J S, Andersen U L 2020 Nat. Phys. 16 281
Google Scholar
[35] Bai S Y, An J H 2021 Phys. Rev. Lett. 127 083602
Google Scholar
[36] Yan Z H, Wu L, Jia X J, Xie C D, Peng K C 2021 Adv. Quantum Technol. 4 2100071
Google Scholar
[37] Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403
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Google Scholar
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Google Scholar
[41] Kang H J, Han D M, Wang N, Liu Y, Hao S H, Su X L 2021 Photonics Res. 9 1330
Google Scholar
[42] Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Rev. Mod. Phys. 84 621
Google Scholar
[43] Takeno Y, Yukawa M, Yonezawa H, Furusawa A 2007 Opt. Express 15 4321
Google Scholar
[44] Adesso G, Serafini A 2004 Phys. Rev. A 70 022318
Google Scholar
[45] Ou Z Y, Pereira S F, Kimble H J, Peng K C 1992 Phys. Rev. Lett. 68 3663
Google Scholar
[46] Zhou Y Y, Yu J, Yan Z H, Jia X J, Zhang J, Xie C D, Peng K C 2018 Phys. Rev. Lett. 121 150502
Google Scholar
[47] Bougouffa S, Ficek Z 2020 Phys. Rev. A 102 043720
Google Scholar
[48] Xiong S J, Sun Z, Su Q P, Xi Z J, Yang C P 2021 Optica 8 1003
Google Scholar
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