Criterion for a state to be distillable via stochastic incoherent operations

TL;DR

This paper establishes the necessary and sufficient conditions for distilling pure coherent states from mixed states using stochastic incoherent operations, revealing fundamental limits and equivalences in coherence distillation.

Contribution

It provides the first complete characterization of when mixed states can be distilled into pure states via stochastic incoherent operations, clarifying the power of sIOs.

Findings

Any 2-dimensional coherent state is distillable iff it is pure.

A state is n-distillable iff it is 1-distillable.

Distillable states via stochastic maximally incoherent operations are the same as via sIOs.

Abstract

Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this paper, we present the necessary and sufficient conditions under which a mixed state can be distilled into a pure coherent state via stochastic incoherent operations (sIOs). With the help of this result, we further show the following: (i) Any $2$-dimensional coherent state is distillable via sIOs if and only if it is a pure coherent state; (ii) a state $\rho$ is n-distillable via sIOs if and only if it is 1-distillable; and (iii) the set of distillable states via stochastic maximally incoherent operations is identical to the set of distillable states via sIOs. Finally, we analyze the reason why sIO is stronger than stochastic strictly incoherent operations when we use them to distill a coherent state.