Quantum coherence

Li Bao-Min; Hu Ming-Liang; Fan Heng

doi:10.7498/aps.68.20181779

Abstract

Quantum coherence is not only a fundamental concept of quantum mechanics, but also an important physical resource for quantum information processing. Along with the formulation of the resource theoretic framework of quantum coherence, the quantification of coherence is still one of the recent research focuses. Quantum coherence is also very fragile, and the environmental noise usually induces a system to decohere. Hence it is also an important subject to make clear the dynamical behavior and to seek a flexible way of preserving quantum coherence of an open quantum system. Besides, there are many potential applications of quantum coherence in quantum many-body system, quantum thermodynamics, quantum biology and other related fields. We review in this paper the resource theoretic framework for quantifying coherence and the relevant quantum coherence measures defined within this framework which includes the relative entropy of coherence, the l₁ norm of coherence, the entanglement-based measure of coherence, the convex roof measure of coherence, and the robustness of coherence. We also review the dynamical behaviors of quantum coherence for certain open quantum systems, the coherence generating and breaking power of typical quantum channels, and the freezing phenomenon of quantum coherence. Moreover, we exemplify applications of quantum coherence in Deutsch-Jozsa algorithm, Grover search algorithms, and the study of quantum phase transitions in multipartite systems. We hope that these results may provide not only an overview of the relevant field, but also an outlook of the future research direction of this exciting field.

Keywords:

Authors and contacts

1.
Solid State Quantum Information and Computation Laboratory, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
4.
Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Hu Ming-Liang, mingliang0301@163.com

Funds: Project supported by the National Key R&D Program of China (Grant Nos. 2016YFA0302104, 2016YFA0300600), the National Natural Science Foundation of China (Grant Nos. 91536108, 11774406, 11675129), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000).

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References

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[47]	Deutsch D, Jozsa R 1992 Proc. R. Soc. Landon A 439 553 Google Scholar
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[49]	Anand N, Pati A K 2016 arXiv:1611.04542 [quant-ph]
[50]	Shi H L, Liu S Y, Wang X H, Yang W L, Yang Z Y, Fan H 2017 Phys. Rev. A 95 032307 Google Scholar
[51]	Karpat G, Çakmak B, Fanchini F F 2014 Phys. Rev. B 90 104431 Google Scholar
[52]	Chen J J, Cui J, Zhang Y R, Fan H 2016 Phys. Rev. A 94 022112 Google Scholar
[53]	Lei S, Tong P 2016 Quantum Inf. Process. 15 1811 Google Scholar
[54]	Li Y C, Lin H Q 2016 Sci. Rep. 6 26365 Google Scholar
[55]	Malvezzi A L, Karpat G, Çakmak B, Fanchini F F, Debarba T, Vianna R O 2016 Phys. Rev. B 93 184428 Google Scholar
[56]	Faist P, Oppenheim J, Renner R 2015 New J. Phys. 17 043003 Google Scholar
[57]	Misra A, Singh U, Bhattacharya S, Pati A K 2016 Phys. Rev. A 93 052335 Google Scholar

Cited By

[1]	Hu M L, Hu X, Wang J, Peng Y, Zhang Y R, Fan H 2018 Phys. Rep. 762 1 Google Scholar
[2]	Aberg J 2014 Phys. Rev. Lett. 113 150402 Google Scholar
[3]	Lostaglio M, Jennings D, Rudolph T 2015 Nat. Commun. 6 6383 Google Scholar
[4]	Narasimhachar V, Gour G 2015 Nat. Commun. 6 7689 Google Scholar
[5]	Lambert N, Chen Y N, Cheng Y C, Li C M, Chen G Y, Nori F 2013 Nat. Phys. 9 10 Google Scholar
[6]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401 Google Scholar
[7]	Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403 Google Scholar
[8]	Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502 Google Scholar
[9]	Bu K, Anand N, Singh U 2018 Phys. Rev. A 97 032342 Google Scholar
[10]	Yu C S 2017 Phys. Rev. A 95 042337 Google Scholar
[11]	Yuan X, Zhou H, Cao Z, Ma X 2015 Phys. Rev. A 92 022124 Google Scholar
[12]	Qi X, Gao T, Yan F L 2017 J. Phys. A 50 285301 Google Scholar
[13]	Liu C L, Zhang D J, Yu X D, Ding Q M 2017 Quantum Inf. Process. 16 198 Google Scholar
[14]	Bromley T R, Cianciaruso M, Adesso G 2015 Phys. Rev. Lett. 114 210401 Google Scholar
[15]	Hu M L, Fan H 2016 Sci. Rep. 6 29260 Google Scholar
[16]	Zanardi P, Styliaris G, Venuti L C 2017 Phys. Rev. A 95 052306 Google Scholar
[17]	Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865 Google Scholar
[18]	Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404 Google Scholar
[19]	Shao L H, Xi Z, Fan H, Li Y 2015 Phys. Rev. A 91 042120 Google Scholar
[20]	Yao Y, Xiao X, Ge L, Li M, Sun C P 2015 Phys. Rev. A 92 022112 Google Scholar
[21]	Streltsov A, Rana S, Boes P, Eisert J 2017 Phys. Rev. Lett. 119 140402 Google Scholar
[22]	Aberg J 2006 arXiv:0612146 [quant-ph]
[23]	Chitambar E, Gour G 2016 Phys. Rev. Lett. 117 030401 Google Scholar
[24]	Chitambar E, Gour G 2016 Phys. Rev. A 94 052336 Google Scholar
[25]	Marvian I, Spekkens R W 2016 Phys. Rev. A 94 052324 Google Scholar
[26]	de Vincenzo J I, Streltsov A 2017 J. Phys. A 50 045301 Google Scholar
[27]	Yu X D, Zhang D J, Xu G F, Tong D M 2016 Phys. Rev. A 94 060302 Google Scholar
[28]	Du S, Bai Z, Guo Y 2015 Phys. Rev. A 91 052120 Google Scholar
[29]	Peng Y, Jiang Y, Fan H 2016 Phys. Rev. A 93 032326 Google Scholar
[30]	Rastegin A E 2016 Phys. Rev. A 93 032136 Google Scholar
[31]	Hu M L, Fan H 2017 Phys. Rev. A 95 052106 Google Scholar
[32]	Yao Y, Dong G H, Ge L, Li M, Sun C P 2016 Phys. Rev. A 94 062339 Google Scholar
[33]	Singh U, Bera M N, Dhar H S, Pati A K 2015 Phys. Rev. A 91 052115 Google Scholar
[34]	Rana S, Parashar P, Lewenstein M 2016 Phys. Rev. A 93 012110 Google Scholar
[35]	Streltsov A, Kampermann H, Bruß D 2010 New J. Phys. 12 123004 Google Scholar
[36]	Marvian I, Spekkens R W 2014 Nat. Commun. 5 3821 Google Scholar
[37]	Marvian I, Spekkens R W, Zanardi P 2016 Phys. Rev. A 93 052331 Google Scholar
[38]	Zhang Y R, Shao LH, Li Y, Fan H 2016 Phys. Rev. A 93 012334 Google Scholar
[39]	Xu J 2016 Phys. Rev. A 93 032111 Google Scholar
[40]	Tan K C, Volkoff T, Kwon H, Jeong H 2017 Phys. Rev. Lett. 119 190405 Google Scholar
[41]	Silva I A, Souza A M, Bromley T R, Cianciaruso M, Marx R, Sarthour R S, Oliveira I S, Franco R L, Glaser S J, deAzevedo E R, Soares-Pinto D O, Adesso G 2016 Phys. Rev. Lett. 117 160402 Google Scholar
[42]	Mani A, Karimipour V 2015 Phys. Rev. A 92 032331 Google Scholar
[43]	Bu K, Kumar A, Zhang L, Wu J 2017 Phys. Lett. A 381 1670 Google Scholar
[44]	Xi Z J, Hu M L, Li Y M, Fan H 2018 Quantum Inf. Process. 17 34 Google Scholar
[45]	Situ H, Hu X 2016 Quantum Inf. Process. 15 4649 Google Scholar
[46]	Andersson E, Cresser J D, Hall M J W 2007 J. Mod. Opt. 54 1695 Google Scholar
[47]	Deutsch D, Jozsa R 1992 Proc. R. Soc. Landon A 439 553 Google Scholar
[48]	Hillery M 2016 Phys. Rev. A 93 012111 Google Scholar
[49]	Anand N, Pati A K 2016 arXiv:1611.04542 [quant-ph]
[50]	Shi H L, Liu S Y, Wang X H, Yang W L, Yang Z Y, Fan H 2017 Phys. Rev. A 95 032307 Google Scholar
[51]	Karpat G, Çakmak B, Fanchini F F 2014 Phys. Rev. B 90 104431 Google Scholar
[52]	Chen J J, Cui J, Zhang Y R, Fan H 2016 Phys. Rev. A 94 022112 Google Scholar
[53]	Lei S, Tong P 2016 Quantum Inf. Process. 15 1811 Google Scholar
[54]	Li Y C, Lin H Q 2016 Sci. Rep. 6 26365 Google Scholar
[55]	Malvezzi A L, Karpat G, Çakmak B, Fanchini F F, Debarba T, Vianna R O 2016 Phys. Rev. B 93 184428 Google Scholar
[56]	Faist P, Oppenheim J, Renner R 2015 New J. Phys. 17 043003 Google Scholar
[57]	Misra A, Singh U, Bhattacharya S, Pati A K 2016 Phys. Rev. A 93 052335 Google Scholar

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Vol. 68, Issue 3 - 2019-02-05

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