Quantum coherence, time-translation symmetry and thermodynamics

Abstract

The first law of thermodynamics imposes not just a constraint on the energy-content of systems in extreme quantum regimes, but also symmetry-constraints related to the thermodynamic processing of quantum coherence. We show that this thermodynamic symmetry decomposes any quantum state into mode operators that quantify the coherence present in the state. We then establish general upper and lower bounds for the evolution of quantum coherence under arbitrary thermal operations, valid for any temperature. We identify primitive coherence manipulations and show that the transfer of coherence between energy levels manifests irreversibility not captured by free energy. Moreover, the recently developed thermo-majorization relations on block-diagonal quantum states are observed to be special cases of this symmetry analysis.

11 pages, 6 figures. Published version. Improved and expanded discussion

References in corpus (3)

• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Extracting work from quantum systems

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