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arXiv · 1707.08795

Max- relative entropy of coherence: an operational coherence measure

Kaifeng Bu·Uttam Singh·Shao-Ming Fei·Arun Kumar Pati·Junde Wu
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Abstract

The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-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 max-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 max-relative entropy of coherence. By introducing suitable smooth max-relative entropy of coherence, we prove that the smooth max-relative entropy of coherence provides a lower bound of one-shot coherence cost, and the max-relative entropy of coherence is equivalent to the relative entropy of coherence in asymptotic limit. Similar to max-relative entropy of coherence, min-relative entropy of coherence has also been investigated. We show that the min-relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in asymptotic limit the min-relative entropy of coherence is equivalent to the relative entropy of coherence.

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Kaifeng Bu, Uttam Singh, Shao-Ming Fei, Arun Kumar Pati, Junde Wu. 2018-01-16. Max- relative entropy of coherence: an operational coherence measure. https://doi.org/10.1103/physrevlett.119.150405

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