Probabilistic distillation of quantum coherence

TL;DR

This paper introduces a probabilistic framework for distilling quantum coherence, revealing fundamental limits, computational methods, and the advantages of catalytic assistance in quantum information processing.

Contribution

It develops a general one-shot probabilistic distillation framework, compares different free operations, and demonstrates the potential of catalysts for enhanced coherence distillation.

Findings

DIO and SIO have equal power in pure state distillation

MIO is strictly stronger than DIO and SIO

Distillation from full-rank states is impossible even probabilistically

Abstract

The ability to distill quantum coherence is pivotal for optimizing the performance of quantum technologies; however, such a task cannot always be accomplished with certainty. Here we develop a general framework of probabilistic distillation of quantum coherence in a one-shot setting, establishing fundamental limitations for different classes of free operations. We first provide a geometric interpretation for the maximal success probability, showing that under maximally incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO) the problem can be simplified into efficiently computable semidefinite programs. Exploiting these results, we find that DIO and its subset of strictly incoherent operations (SIO) have equal power in probabilistic distillation of coherence from pure input states, while MIO are strictly stronger. We then prove a fundamental no-go result: distilling coherence from any full-rank state is impossible even probabilistically. We further find that in some conditions the maximal success probability can vanish suddenly beyond a certain threshold in the distillation fidelity. Finally, we consider probabilistic coherence distillation assisted by a catalyst and demonstrate, with specific examples, its superiority to the unassisted and deterministic cases.