Maximum coherence under noisy channels

Abstract

For the well-known relative entropy of coherence (REC), a quantum state attains maximum coherence only in optimal bases, which are mutually unbiased bases to the eigenvectors of the given state. In this paper, we explore the conditions of obtaining the maximum of REC under noisy channels and explain the geometric significance of optimal basis form the viewpoint of the Bloch sphere. We also show that the eigenvectors of the state will remain constant throughout the whole process of evolution, as long as the effects of channels induce a synchronous change for the components of the initial state Bloch vector. Furthermore, as a special example, we investigate the dynamics of the maximum REC for any finite dimensional single quantum system under a depolarizing (DP) channel, and obtain an analytical form of maximum coherence for a d-dimensional maximally coherent state. Meanwhile, a concise analytical expression of maximum coherence for two classes of an N-qubit system under the DP channel is also provided.