# Markovian evolution of quantum coherence under symmetric dynamics

## TL;DR

This paper explores the limits of quantum coherence preservation under symmetric, Markovian dynamics, generalizing known decoherence bounds, and linking resource theory with thermodynamics in quantum systems.

## Contribution

It identifies minimal decoherence constraints under energy-translation symmetry and connects resource theory with master equations in quantum thermodynamics.

## Key findings

- Generalized the $T_2 \,\leq\, 2 T_1$ relation to higher dimensions
- Provided criteria to witness non-Markovianity as a coherence resource
- Linked resource-theoretic and master equation approaches to quantum thermodynamics

## Abstract

Both conservation laws and practical restrictions impose symmetry constraints on the dynamics of open quantum systems. In the case of time-translation symmetry, which arises naturally in many physically relevant scenarios, the quantum coherence between energy eigenstates becomes a valuable resource for quantum information processing. In this work we identify the minimum amount of decoherence compatible with this symmetry for a given population dynamics. This yields a generalisation to higher-dimensional systems of the relation $T_2 \leq 2 T_1$ for qubit decoherence and relaxation times. It also enables us to witness and assess the role of non-Markovianity as a resource for coherence preservation and transfer. Moreover, we discuss the relationship between ergodicity and the ability of Markovian dynamics to indefinitely sustain a superposition of different energy states. Finally, we establish a formal connection between the resource-theoretic and the master equation approaches to thermodynamics, with the former being a non-Markovian generalisation of the latter. Our work thus brings the abstract study of quantum coherence as a resource towards the realm of actual physical applications.