多体系统中相干资源的一般化理论

刘锋; 高冬梅; 蔡晓秋

doi:10.7498/aps.68.20190966

摘要

量子相干理论是一类重要的量子资源理论, 其自由操作是各种类型的非相干操作. 在单体相干资源理论中, 最大相干态是最重要的量子资源态, 它被定义为在非相干操作下可以转化为任何其他纯态的量子态. 但是, 这一情形在多体系统中发生了巨大改变: 不仅在有些相干度量下不存在唯一的最大相干态, 而且在有些非相干操作下几乎所有纯的相干多体态都不可比较(非相干操作下, 量子态之间的转换几乎不可能). 为了解决这一问题, 把非相干操作的定义扩展为一种不能产生相干的量子操作, 即研究一般化的相干资源理论. 具体地说, 基于量子资源是否来源于多体相干或者真的多体相干研究两类可能的量子资源理论框架, 并且指出在这些理论框架下存在合理的偏序关系(每个纯态都可在非相干操作下转换为相干度更弱的纯态). 另外, 还证明了真的多体相干资源理论下存在唯一的最大相干态.

关键词:

Abstract

The theory of quantum coherence is an important kind of quantum resource theory, and its free operations are various kinds of incoherent operations. In the single-system coherence resource theory, the maximally coherent state is the most important quantum resource state, and it can turn into a quantum state of any other pure state. However, the situation is quite different from multipartite quantum systems: not only does no-go theorem forbidding the existence of a unique maximally coherent state exist there, but almost all pure multipartite coherent states are incomparable (i.e., some incoherent operation transformations among them are almost never possible). In order to cope with this problem, we consider general coherent resource theories in which we relax the traditional incoherent operations to operations that do not create coherence. Specifically, we consider two possible theories, depending on whether resources correspond to bipartite coherence or genuinely multipartite coherent states (each subsystem is coherent): one is the theory in which bipartite coherence states are considered as a resource and the free operations are bipartite incoherent preservation and the other is the theory that involves genuinely multipartite coherent states and fully incoherent operations. These ideas come from the research by Contreras-Tejada et al. (Phys. Rev. Lett. 122 120503), where the alternative entanglement resource theories were considered through relaxing the class of local operations and classical communication (LOCC) to operations that do not create entanglement, and they considered two possible theories depending on whether resources correspond to the multipartite entangled or genuinely multipartite entangled (GME) states. Furthermore, we show that there exists meaningful partial order (i.e. each pure state is transformable to a more weakly coherent pure state) in these two theory frames. Finally, we prove that the genuine multipartite coherent resource theory has a unique maximally coherent state (i.e. it can be transformed into any other state by the allowed free operations). Our results cover a wide class of coherent resource theories due to the free operations we introduced, and the discussion is solidified by important examples, such as entanglement, superposition, asymmetry, et al. And, how to establish the relations between these two kinds of multipartite coherent states, quantum discords and entanglements is also an interesting problem.

Keywords:

作者及机构信息

1.
山东工商学院数学与信息科学学院, 烟台　264005

2.
北京邮电大学网络技术研究院, 北京　100876

3.
洛阳师范学院数学科学学院, 洛阳　471934

通信作者: 刘锋, liufeng23490@126.com

基金项目: 国家自然科学基金(批准号: 61771294, 61602232)和山东省自然科学基金(批准号: ZR2015FQ006)资助的课题.

Authors and contacts

1.
School of Mathematic and Information Science, Shandong Technology and Business Universiy, Yantai 264005, China

2.
Institute of Network Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China

3.
School of Mathematic Science, Luoyang Normal University, Luoyang 471934, China

Corresponding author: Liu Feng, liufeng23490@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61771294, 61602232) and the Natural Science Foundation of Shandong Provincie, China (Grant No. ZR2015FQ006)

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参考文献

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施引文献

[1]	Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865 Google Scholar
[2]	Chitambar E, Gour G 2019 Rev. Mod. Phys. 91 025001 Google Scholar
[3]	Streltsov A, Adesso G, Plenio M B 2017 Rev. Mod. Phys. 89 041003 Google Scholar
[4]	Hu M L, Hu X, Wang J, Peng Y, Zhang Y R, Fan H 2018 Phys. Rep. 762–764 1 Google Scholar
[5]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401 Google Scholar
[6]	Winter A, Yang D 2016 Phys. Rev. Lett. 116 120404 Google Scholar
[7]	Zhao M J, Ma T, Quan Q, Fan H, Pereira R 2019 Phys. Rev. A 100 012315 Google Scholar
[8]	Zhou Y, Zhao Q, Yuan X, Ma X 2017 New J. Phys. 19 123033 Google Scholar
[9]	Yao Y, Xiao X, Ge L, Sun C P 2015 Phys. Rev. A 92 022112 Google Scholar
[10]	Streltsov A, Rana S, Bera M N, Lewenstein M 2017 Phys. Rev. X 7 011024
[11]	Kumar A 2017 Phys. Lett. A 381 991 Google Scholar
[12]	Gao F, Qin S J, Huang W, Wen Q Y 2019 Sci. China-Phys. Mech. Astron. 62 070301 Google Scholar
[13]	杨宇光, 张兴 2008 中国科学: 物理学力学天文学 38 523 Yang Y G, Zhang X 2008 Sci. Sin.-Phys. Mech. Astron. 38 523
[14]	Wei C Y, Cai X Q, Liu B, Wang T Y, Gao F 2018 IEEE Trans. Comput. 67 2 Google Scholar
[15]	Ma J, Zhou Y, Yuan X, Ma X 2019 Phys. Rev. A 99 062325 Google Scholar
[16]	Ma J, Hakande A, Yuan X, Ma X 2019 Phys. Rev. A 99 022328 Google Scholar
[17]	Walther P, Resch K J, Rudolph T, Schenck E, Weinfurter H, Vedral V, Aspelmeyer M, Zeilinger A 2005 Nature 434 169 Google Scholar
[18]	Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188 Google Scholar
[19]	Pan M, Qiu D 2019 Phys. Rev. A 100 012349 Google Scholar
[20]	李海, 邹健, 邵彬, 陈雨, 华臻 2019 68 040201 Google Scholar Li H, Zou J, Shao B, Chen Y, Hua Z 2019 Acta Phys. Sin. 68 040201 Google Scholar
[21]	Gao D M, Xin Y, Ye Z, Qiao X Y 2019 Int. J. Quantum Inf. 17 1950004 Google Scholar
[22]	Liu F, Li F 2016 Quantum Inf. Process 15 4203 Google Scholar
[23]	Liu F, Li F, Chen J, Xing W 2016 Quantum Inf. Process 15 3459 Google Scholar
[24]	Lostaglio M, Müller M P 2019 Phys. Rev. Lett. 123 020403 Google Scholar
[25]	Luo S, Sun Y 2019 Phys. Lett. A 383 2869 Google Scholar
[26]	Zhao Q, Liu Y, Yuan X, Chitambar E, Ma X 2018 Phys. Rev. Lett. 120 070403 Google Scholar
[27]	Brunner N, Cavalcanti D, Pironio S, Scarani V, Wehner S 2014 Rev. Mod. Phys. 86 419 Google Scholar
[28]	Gallego R, Aolita L 2015 Phys. Rev. X 5 041008
[29]	肖书, 郭志华, 曹怀信 2019 中国科学: 物理学力学天文学 49 010301 Xiao S, Guo Z H, Cao H X 2019 Sci. Sin.-Phys. Mech Astron 49 010301
[30]	Lami L, Regula B, Adesso G 2019 Phys. Rev. Lett. 122 150402 Google Scholar
[31]	Wu K D, Theurer T, Xiang G Y, Li C F, Guo G C, Plenio M B, Streltsov A 2019 arXiv: 1903.01479 v1 [quant-ph]
[32]	Du S, Bai Z, Guo Y 2017 Phys. Rev. A 95 029901 Google Scholar
[33]	Brandão F G S L, Plenio M B 2008 Nat. Phys. 4 873 Google Scholar
[34]	Contreras-Tejada P, Palazuelos C, de Vicente J I 2019 Phys. Rev. Lett. 122 120503 Google Scholar
[35]	Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502 Google Scholar
[36]	Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403 Google Scholar
[37]	Chitambar E, de Vicente J I, Girard M W, Gour G 2017 arXiv: 1711.03835 [quant-ph]
[38]	Vidal G, Tarrach R 1999 Phys. Rev. A 59 141 Google Scholar
[39]	Sauerwein D, Wallach N R, Gour G, Kraus B 2018 Phys. Rev. X 8 031020
[40]	Hebenstreit M, Spee C, Kraus B 2016 Phys. Rev. A 92 012339 Google Scholar
[41]	Wei T C, Goldbart P M 2003 Phys. Rev. A 68 042307 Google Scholar
[42]	Chen L, Xu A, Zhu H 2010 Phys. Rev. A 82 032301 Google Scholar
[43]	Eisert J, Brandao F G, Audenaert K M 2007 New J. Phys. 9 46 Google Scholar
[44]	Dür W, Cirac J I, Tarrach R 1999 Phys. Rev. Lett. 83 3562 Google Scholar
[45]	Zhu H, Ma Z, Cao Z, Fei S M, Vedral V 2017 Phys. Rev. A 96 032316 Google Scholar
[46]	Biswas A, Prabhu R, de Sen A, Sen U 2014 Phys. Rev. A 90 032301 Google Scholar

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