Quantum coherence fluctuation relations

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.

22 pages, 1 figure; to appear in Journal of Physics A - Special Issue on Quantum Coherence

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• The first law of general quantum resource theories
• Coherence manipulation with dephasing-covariant operations
• Information Fluctuation Theorem for an Open Quantum Bipartite System
• Thermodynamics of relativistic quantum fields confined in cavities
• Decomposable coherence and quantum fluctuation relations
• Quantum fluctuation theorem for initial near-equilibrium system
• Quantum entanglement and extractable work for Gaussian states