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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.
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[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 物理学报 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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