Assisted coherence distillation of certain mixed states

TL;DR

This paper investigates assisted coherence distillation for specific mixed states, showing equivalence of various operation sets and identifying conditions where assistance does or does not enhance Bob's coherence.

Contribution

It demonstrates the equivalence of four operation sets in assisted coherence distillation for certain mixed states and establishes when assistance can reach the theoretical maximum coherence.

Findings

All four operation sets are equivalent for the states considered.

Assisted coherence distillation can reach the QI relative entropy upper bound for some states.

Assistance does not improve coherence if the shared state has vanished basis-dependent discord.

Abstract

In the task of assisted coherence distillation via the set of operations X, where X is either local incoherent operations and classical communication (LICC), local quantum-incoherent operations and classical communication (LQICC), separable incoherent operations (SI), or separable quantum incoherent operations (SQI), two parties, namely Alice and Bob, share many copies of a bipartite joint state. The aim of the process is to generate the maximal possible coherence on the subsystem of Bob. In this paper, we investigate the assisted coherence distillation of some special mixed states, the states with vanished basis-dependent discord and Werner states. We show that all the four sets of operations are equivalent for assisted coherence distillation, whenever Alice and Bob share one of those mixed quantum states. Moreover, we prove that the assisted coherence distillation of the former can reach the upper bound, namely QI relative entropy, while that of the latter can not. Meanwhile, we also present a sufficient condition such that the assistance of Alice via the set of operations X can not help Bob improve his distillable coherence, and this condition is that the state shared by Alice and Bob has vanished basis-dependent discord.