Markovian evolution of quantum coherence under symmetric dynamics
Matteo Lostaglio, Kamil Korzekwa, Antony Milne · Physical Review A · 2017
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 generalization to higher-dimensional systems of the relation ${T}_{2}\ensuremath{\le}2{T}_{1}$ 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 generalization of the latter. Our work thus brings the abstract study of quantum coherence as a resource towards the realm of actual physical applications.