One-shot coherence distillation

TL;DR

This paper investigates the process of extracting maximal quantum coherence from states in a single-shot scenario, revealing that certain classes of quantum operations are equally powerful and providing computable measures for coherence distillation.

Contribution

It demonstrates the equivalence of MIO and DIO in one-shot coherence distillation and introduces new coherence monotones with operational meaning.

Findings

MIO and DIO have the same power in one-shot coherence distillation.

The one-shot distillable coherence is efficiently computable via semidefinite programming.

Explicit formulas for coherence monotones for pure states are provided.

Abstract

We characterize the distillation of quantum coherence in the one-shot setting, that is, the conversion of general quantum states into maximally coherent states under different classes of quantum operations. We show that the maximally incoherent operations (MIO) and the dephasing-covariant incoherent operations (DIO) have the same power in the task of one-shot coherence distillation. We establish that the one-shot distillable coherence under MIO and DIO is efficiently computable with a semidefinite program, which we show to correspond to a quantum hypothesis testing problem. Further, we introduce a family of coherence monotones generalizing the robustness of coherence as well as the modified trace distance of coherence, and show that they admit an operational interpretation in characterizing the fidelity of distillation under different classes of operations. By providing an explicit formula for these quantities for pure states, we show that the one-shot distillable coherence under MIO, DIO, strictly incoherent operations (SIO), and incoherent operations (IO) is equal for all pure states.