Maximum Relative Entropy of Coherence for Quantum Channels

TL;DR

This paper introduces a new coherence quantifier for quantum channels based on maximum relative entropy, providing operational interpretations and linking it to channel discrimination advantages and robustness measures.

Contribution

It defines a novel coherence measure for quantum channels via maximum relative entropy and explores its operational significance and relation to other coherence measures.

Findings

Maximum relative entropy quantifies coherence of quantum channels.

Operational interpretation linked to maximally coherent channels.

Characterizes advantage in sub-superchannel discrimination.

Abstract

Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum channels is directly related to the maximally coherent channels under a particular class of superoperations, which results in an operational interpretation of the maximum relative entropy for coherence of quantum channels. We also introduce the conception of sub-superchannels and sub-superchannel discrimination. For any quantum channels, we show that the advantage of quantum channels in sub-superchannel discrimination can be exactly characterized by the maximum relative entropy of coherence for quantum channels. Similar to the maximum relative entropy of coherence for channels, the robustness of coherence for quantum channels has also been investigated. We show that the maximum relative entropy of coherence for channels provides new operational interpretations of robustness of coherence for quantum channels and illustrates the equivalence of the dephasing-covariant superchannels, incoherent superchannels, and strictly incoherent superchannels in these two operational tasks.