Coherence of assistance and regularized coherence of assistance

TL;DR

This paper explores the relationship between coherence of assistance and its regularized form, providing conditions for their equivalence, analyzing examples, and proposing a protocol for maximizing relative entropy coherence with assistance.

Contribution

It establishes necessary and sufficient conditions for the coherence of assistance to match its regularized version and introduces a protocol for maximizing coherence with assistance.

Findings

Conditions for coherence quantities to coincide are derived.

Optimal pure state decompositions are characterized.

A protocol for maximal relative entropy coherence with assistance is proposed.

Abstract

We study the relation between the coherence of assistance and the regularized coherence of assistance introduced by Chitambar et al. [E. Chitambar et al., Phys. Rev. Lett. 116, 070402 (2016)]. The necessary and sufficient conditions that these two quantities coincide are provided. Detailed examples are analyzed and the optimal pure state decompositions such that the coherence of assistance equals the regularized coherence of assistance are derived. Moreover, we present the protocol for obtaining the maximal relative entropy coherence, assisted by another party under local measurement and one-way communication in one copy setting.