Conditions for coherence transformations under incoherent operations

TL;DR

This paper establishes a fundamental theorem for coherence transformations under incoherent operations, revealing different types of coherence, the catalytic role of certain states, and implications for coherence measures.

Contribution

It provides a Nielsen-like theorem for coherence, introduces coherence catalysts, and advances understanding of coherence manipulation and measurement.

Findings

Existence of different types of coherence.

Incoherent operations can be catalyzed by coherent states.

New insights into coherence measures and transformations.

Abstract

We build the counterpart of the celebrated Nielsen's theorem for coherence manipulation in this paper. This offers an affirmative answer to the open question: whether, given two states $\rho$ and $\sigma$, either $\rho$ can be transformed into $\sigma$ or vice versa under incoherent operations [Phys. Rev. Lett. \textbf{113}, 140401(2014)]. As a consequence, we find that there exist essentially different types of coherence. Moreover, incoherent operations can be enhanced in the presence of certain coherent states. These extra states are coherent catalysts: they allow uncertain incoherent operations to be realized, without being consumed in any way. Our main result also sheds a new light on the construction of coherence measures.