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 based on permutation matrices that, acting on the initial state of the system, (i) suppress the contribution of slowest decaying modes of the nonunitary dynamics; (ii) ensure that it is as distinguishable as possible from the steady state. The first requirement guarantees an exponentially accelerating convergence to the steady state, while the second implies that a quantum system initially farther from equilibrium approaches it more rapidly than an initial state closer to it. This protocol provides a genuine Mpemba effect, and its numerical simulation requires low computational effort. We prove that, for any initial state, there always exists a permutation matrix that maximizes its distance from the equilibrium for a given information-theoretic distinguishability measure. We illustrate our findings for the nonunitary dynamics of the transverse field Ising chain and XXZ chain, each weakly coupled to a bosonic thermal bath, showing the quantum Mpemba effect captured by the Hilbert-Schmidt distance, quantum relative entropy, and trace distance. Our results provide a universal and versatile framework to engineer the genuine quantum Mpemba effect in open quantum systems.