Maximum Relative Entropy of Coherence: An Operational Coherence Measure

Physical Review Letters
Kaifeng BuJunde Wu

Abstract

The operational characterization of quantum coherence is the cornerstone in the development of the resource theory of coherence. We introduce a new coherence quantifier based on maximum relative entropy. We prove that the maximum relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of the maximum relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the maximum relative entropy of coherence. By introducing a suitable smooth maximum relative entropy of coherence, we prove that the smooth maximum relative entropy of coherence provides a lower bound of one-shot coherence cost, and the maximum relative entropy of coherence is equivalent to the relative entropy of coherence in the asymptotic limit. Similar to the maximum relative entropy of coherence, the minimum relative entropy of cohe...Continue Reading

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Citations

Jul 22, 2018·Physical Review Letters·Bartosz RegulaGerardo Adesso
Aug 7, 2019·Physical Review Letters·Zi-Wen LiuRyuji Takagi
Sep 7, 2019·Physical Review Letters·C L Liu, D L Zhou
May 6, 2019·Physical Review Letters·Ryuji TakagiGerardo Adesso
Oct 2, 2019·Physical Review Letters·Felix BischofDagmar Bruß
Apr 18, 2021·Physical Review. E·Diego Paiva PiresLucas Chibebe Céleri

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