Optimal probabilistic distillation of quantum coherence

TL;DR

This paper develops an optimal probabilistic protocol for transforming quantum states into maximally coherent states using strictly incoherent operations, providing analytical bounds and a universal approach applicable to any coherence measure.

Contribution

It introduces necessary and sufficient conditions for state transformation via SIO and presents an analytical expression for maximal distillable coherence, advancing quantum coherence manipulation.

Findings

Derived the necessary and sufficient condition for state transformation via SIO.

Provided an analytical expression for maximal average distillable coherence.

Developed a universal protocol applicable to any coherence measure.

Abstract

We complete the task of optimal probabilistic coherence distillation protocol, whose aim is to transform a general state into a set of n-level maximally coherent states via strictly incoherent operations (SIO). Specifically, we present the necessary and sufficient condition for the transformation from a mixed state into a pure-state ensemble via SIO. With the aid of this condition and the simplex algorithm, we can accomplish the probabilistic distillation protocol by presenting an analytical expression of the maximal average distillable coherence of a general state and constructing the corresponding operation achieving this bound. Our protocol is a universal protocol since it can be applied to any coherence measure.