Quantumness of ensembles via coherence

Abstract

The notion of quantum ensembles is necessary for a description of quantum systems with incomplete information, which often occurs in the theory of quantum measurement and communication. Since ensembles involving non-commuting states possess intrinsic quantumness and play a central role in various quantum information processing tasks, it is desirable to quantify the quantum characteristics in ensembles from different points of view. In this paper, we define a quantifier for quantumness of quantum ensembles from the perspective of coherence, and prove this quantifier satisfies almost all natural desiderata for a measure of quantumness recently suggested by Li et al. (2017) [12]. Furthermore, this measure also possesses monotonicity under commutativity preserving operations, which intrigues a discussion on the resource theory of quantumness. We find that this measure is equivalent to the quantumness measures proposed formerly via correlation and relative entropy, by which they share these properties.