Quantum coherence fluctuation relations

TL;DR

This paper derives fluctuation relations for quantum coherence using a coherence battery, establishing coherence as a physical resource and connecting it to thermodynamic fluctuation theorems.

Contribution

It introduces fluctuation relations for quantum coherence with a coherence battery, linking resource theories and thermodynamics in quantum systems.

Findings

Derived quantum coherence fluctuation relations analogous to thermodynamic ones.

Connected coherence resource theory with fluctuation theorems.

Provided insights into battery-assisted quantum resource theories.

Abstract

We investigate manipulations of pure quantum states under incoherent or strictly incoherent operations assisted by a coherence battery, that is, a storage device whose degree of coherence is allowed to fluctuate in the process. This leads to the derivation of fluctuation relations for quantum coherence, analogous to Jarzynski's and Crooks' relations for work in thermodynamics. Coherence is thus revealed as another instance of a physical resource, in addition to athermality and entanglement, for which a connection is established between the majorisation framework (regulating pure state transformations under suitable free operations) and the emergence of fluctuation theorems. Our study is hoped to provide further insight into the general structure of battery assisted quantum resource theories, and more specifically into the interplay between quantum coherence and quantum thermodynamics.