Genuine quantum coherence

TL;DR

This paper introduces a new framework for quantum coherence based on genuinely incoherent operations that preserve all incoherent states, analyzing their structure and limitations in state transformations.

Contribution

It proposes the concept of genuine quantum coherence and fully incoherent operations, providing a detailed mathematical analysis and highlighting limitations in deterministic state manipulation.

Findings

Deterministic manipulation of coherence is severely limited.

No single state acts as a universal resource (no golden unit).

Genuine incoherent operations are invariant across experimental realizations.

Abstract

Any quantum resource theory is based on free states and free operations, i.e., states and operations which can be created and performed at no cost. In the resource theory of coherence free states are diagonal in some fixed basis, and free operations are those which cannot create coherence for some particular experimental realization. Recently, some problems of this approach have been discussed, and new sets of operations have been proposed to resolve these problems. We propose here the framework of genuine quantum coherence. This approach is based on a simple principle: we demand that a genuinely incoherent operation preserves all incoherent states. This framework captures coherence under additional constrains such as energy preservation and all genuinely incoherent operations are incoherent regardless of their particular experimental realization. We also introduce the full class of operations with this property, which we call fully incoherent. We analyze in detail the mathematical structure of these classes and also study possible state transformations. We show that deterministic manipulation is severely limited, even in the asymptotic settings. In particular, this framework does not have a unique golden unit, i.e., there is no single state from which all other states can be created deterministically with the free operations. This suggests that any reasonably powerful resource theory of coherence must contain free operations which can potentially create coherence in some experimental realization.