Coherence measures based on coherence eigenvalue and their applications

Abstract

The quantification of coherence is central in quantum information theory and far from being fully understood, particularly for multipartite quantum states. In this work, we first propose the coherence eigenvalue for multipartite pure quantum states and then define the coherence measure for a given multipartite pure or mixed state based on it. It is found that the convex roof coherence measure is equal to the geometric measure based on fidelity. This finding allows us to give an alternative way to prove that the geometric measure of coherence is monotone under selective measurements on average. The other two new coherence measures based on coherence eigenvalue are presented, and their properties are also investigated. As an application, the bounds of several well-known coherence measures are derived by using of coherence eigenvalue. In particular, by proposing a new coherence witness which is related to coherence eigenvalue, we obtain a bound to robustness of coherence and give it a corresponding geometric interpretation.