Coherence of assistance and assisted maximally coherent states

Abstract Coherence and entanglement are fundamental concepts in resource theory. The coherence (entanglement) of assistance is the coherence (entanglement) that can be extracted assisted by another party with local measurement and classical communication. We introduce and study the general coherence...

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Autores principales:	Ming-Jing Zhao, Rajesh Pereira, Teng Ma, Shao-Ming Fei
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/34af4e1eed054f2ca50040f8ee3d3d29
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spelling	oai:doaj.org-article:34af4e1eed054f2ca50040f8ee3d3d292021-12-02T13:18:08ZCoherence of assistance and assisted maximally coherent states10.1038/s41598-021-85273-82045-2322https://doaj.org/article/34af4e1eed054f2ca50040f8ee3d3d292021-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-85273-8https://doaj.org/toc/2045-2322Abstract Coherence and entanglement are fundamental concepts in resource theory. The coherence (entanglement) of assistance is the coherence (entanglement) that can be extracted assisted by another party with local measurement and classical communication. We introduce and study the general coherence of assistance. First, in terms of real symmetric concave functions on the probability simplex, the coherence of assistance and the entanglement of assistance are shown to be in one-to-one correspondence. We then introduce two classes of quantum states: the assisted maximally coherent states and the assisted maximally entangled states. They can be transformed into maximally coherent or entangled pure states with the help of another party using local measurement and classical communication. We give necessary conditions for states to be assisted maximally coherent or assisted maximally entangled. Based on these, a unified framework between coherence and entanglement including coherence (entanglement) measures, coherence (entanglement) of assistance, coherence (entanglement) resources is proposed. Then we show that the coherence of assistance as well as entanglement of assistance are strictly larger than the coherence of convex roof and entanglement of convex roof for all full rank density matrices. So all full rank quantum states are distillable in the assisted coherence distillation.Ming-Jing ZhaoRajesh PereiraTeng MaShao-Ming FeiNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-8 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Ming-Jing Zhao Rajesh Pereira Teng Ma Shao-Ming Fei Coherence of assistance and assisted maximally coherent states
description	Abstract Coherence and entanglement are fundamental concepts in resource theory. The coherence (entanglement) of assistance is the coherence (entanglement) that can be extracted assisted by another party with local measurement and classical communication. We introduce and study the general coherence of assistance. First, in terms of real symmetric concave functions on the probability simplex, the coherence of assistance and the entanglement of assistance are shown to be in one-to-one correspondence. We then introduce two classes of quantum states: the assisted maximally coherent states and the assisted maximally entangled states. They can be transformed into maximally coherent or entangled pure states with the help of another party using local measurement and classical communication. We give necessary conditions for states to be assisted maximally coherent or assisted maximally entangled. Based on these, a unified framework between coherence and entanglement including coherence (entanglement) measures, coherence (entanglement) of assistance, coherence (entanglement) resources is proposed. Then we show that the coherence of assistance as well as entanglement of assistance are strictly larger than the coherence of convex roof and entanglement of convex roof for all full rank density matrices. So all full rank quantum states are distillable in the assisted coherence distillation.
format	article
author	Ming-Jing Zhao Rajesh Pereira Teng Ma Shao-Ming Fei
author_facet	Ming-Jing Zhao Rajesh Pereira Teng Ma Shao-Ming Fei
author_sort	Ming-Jing Zhao
title	Coherence of assistance and assisted maximally coherent states
title_short	Coherence of assistance and assisted maximally coherent states
title_full	Coherence of assistance and assisted maximally coherent states
title_fullStr	Coherence of assistance and assisted maximally coherent states
title_full_unstemmed	Coherence of assistance and assisted maximally coherent states
title_sort	coherence of assistance and assisted maximally coherent states
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/34af4e1eed054f2ca50040f8ee3d3d29
work_keys_str_mv	AT mingjingzhao coherenceofassistanceandassistedmaximallycoherentstates AT rajeshpereira coherenceofassistanceandassistedmaximallycoherentstates AT tengma coherenceofassistanceandassistedmaximallycoherentstates AT shaomingfei coherenceofassistanceandassistedmaximallycoherentstates
_version_	1718393263151382528

Coherence of assistance and assisted maximally coherent states

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