Engineering quantum Mpemba effect by Liouvillian skin effect

We propose a novel approach to engineer the quantum Mpemba effect (QME)-wherein an initial state farther from the steaty state relaxes faster than a closer one-by the Liouvillian skin effect (LSE) in open quantum systems. We show that, in the open quantum chain with LSE, QME can be easily realized by considering only the spatial profile of initial states, since the initial states localized on the left or right edges experience distinctive relaxation process (algebraic or exponential decay). This approach circumvents the necessity of careful initial-state design and fine-tuning of control parameter. Moreover, when the initial correlation matrix contains off-diagonal elements, we uncover a new kind of QME which manifest as two crossings in the Hilbert-Schmidt distance at different times. This work unveils the deep connection between QME and LSE, and provides a physically intuitive understanding of QME and straightforward pathway for the initial state preparation thereby enabling readily accessible experimental preparation.