Channel-based coherence of quantum states

Abstract

Quantum coherence is one of the most fundamental and striking features in quantum physics. Considered the standard coherence (SC), the partial coherence (PC) and the block coherence (BC) as variance of quantum states under some quantum channels (QCs) [Formula: see text], we propose the concept of channel-based coherence of quantum states, called [Formula: see text]-coherence for short, which contains the SC, PC and BC, but does not contain the positive operator-valued measure (POVM)-based coherence. By our definition, a state [Formula: see text] is said to be [Formula: see text]-incoherent if it is a fixed point of a QC [Formula: see text], otherwise, it is said to be [Formula: see text]-coherent. First, we find the set [Formula: see text] of all [Formula: see text]-incoherent states for some given channels [Formula: see text] and prove that the set [Formula: see text] forms a nonempty compact convex set for any channel [Formula: see text]. Second, we define [Formula: see text]-incoherent operations ([Formula: see text]-IOs) and prove that the set of all [Formula: see text]-IOs is a nonempty convex set. We also establish some characterizations of a [Formula: see text]-IO in terms of its Kraus operators. Lastly, we discuss the problem of quantifying [Formula: see text]-coherence and prove some related properties.