Family of coherence measures and duality between quantum coherence and path distinguishability

Abstract

Coherence measures and their operational interpretations lay the cornerstone of coherence theory. In this paper, we introduce a class of coherence measures with $\alpha$-affinity, say $\alpha$-affinity of coherence for $\alpha \in (0,1)$. Furthermore, we obtain the analytic formulae for these coherence measures and study their corresponding convex roof extension. We provide an operational interpretation for $1/2$-affinity of coherence by showing that it is equal to the error probability to discrimination a set of pure states with the least square measurement. Employing this relationship we regain the optimal measurement for equiprobable quantum state discrimination. Moreover, we compare these coherence quantifiers, and establish a complementarity relation between $1/2$-affinity of coherence and path distinguishability for some special cases.

arXiv comment11 pages, close to published version

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• Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information
• Coherence and complementarity based on modified generalized skew information
• Average skew information-based coherence and its typicality for random quantum states
• Skew information-based coherence generating power of quantum channels
• Geometry of skew information-based quantum coherence
• Quantifying dynamical coherence with coherence measures
• Partial coherence versus entanglement
• Converting coherence based on positive-operator-valued measures into entanglement
• Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
• Coherence measures based on sandwiched Rényi relative entropy
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• Quantumness of pure-state ensembles via coherence of Gram matrix based on generalized $\alpha$-$z$-relative Rényi entropy
• Estimating coherence with respect to general quantum measurements
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