Exponentially accelerated relaxation and quantum Mpemba effect in open quantum systems

Abstract

We investigate the quantum Mpemba effect in the relaxation of open quantum systems whose effective dynamics is described by Davies maps. We present a class of unitary transformations built from permutation matrices that, when applied to the initial state of the system, (i) suppress the slowest decaying modes of the nonunitary dynamics; (ii) maximize its distinguishability from the steady state. The first requirement guarantees exponentially accelerating convergence to the steady state, and the second implies that a quantum system initially farther from equilibrium approaches it more rapidly than one that starts closer. This protocol provides a genuine Mpemba effect, and its numerical simulation requires low computational effort. We prove that, for any initial state, one can always find a permutation matrix that maximizes its distance from equilibrium for a specified information-theoretic distinguishability measure. We illustrate our findings for a two-level system, and also for the nonunitary dynamics of the transverse field Ising chain and XXZ chain, each weakly coupled to a bosonic thermal bath, and demonstrate the quantum Mpemba effect as captured by the Hilbert-Schmidt distance, quantum relative entropy, and trace distance. Our results provide a versatile framework to engineer the genuine quantum Mpemba effect in Markovian open quantum systems.