Quantum coherence, time-translation symmetry and thermodynamics

TL;DR

This paper explores how thermodynamic principles impose symmetry constraints on quantum coherence, deriving bounds on coherence evolution and revealing irreversibility in quantum thermodynamic processes.

Contribution

It introduces a symmetry-based framework for analyzing quantum coherence in thermodynamics, providing bounds and connecting to thermo-majorization relations.

Findings

Decomposition of quantum states into coherence modes.

Bounds on coherence evolution under thermal operations.

Irreversibility in coherence transfer beyond free energy.

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.