Assisted distillation of quantum coherence

TL;DR

This paper introduces assisted coherence distillation in bipartite quantum systems, showing how two parties can collaborate to maximize coherence on one subsystem using specific allowed operations, and links the process to the von Neumann entropy.

Contribution

It defines the task of assisted coherence distillation, characterizes its asymptotic rate for pure states, and relates it to the coherence of assistance, providing a new interpretation of von Neumann entropy.

Findings

Asymptotic rate equals the coherence of assistance.

Von Neumann entropy quantifies maximum coherence gain with assistance.

Generalization to multipartite coherence localization.

Abstract

We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are allowed on the target system while general local quantum operations are permitted on the other, an operational paradigm that we call local quantum-incoherent operations and classical communication (LQICC). We show that the asymptotic rate of assisted coherence distillation for pure states is equal to the coherence of assistance, an analog of the entanglement of assistance, whose properties we characterize. Our findings imply a novel interpretation of the von Neumann entropy: it quantifies the maximum amount of extra quantum coherence a system can gain when receiving assistance from a collaborative party. Our results are generalized to coherence localization in a multipartite setting and possible applications are discussed.