Initial-State Typicality in Quantum Relaxation

TL;DR

This paper reveals that in large open quantum systems, relaxation behavior becomes nearly independent of initial states, especially above a certain temperature, with implications for quantum simulation and state preparation.

Contribution

The study introduces the concept of initial-state typicality in quantum relaxation, extending typicality to open quantum dynamics and providing new insights into relaxation processes.

Findings

Relaxation becomes initial-state-independent in large systems.

Typical relaxation behavior applies above a size-independent temperature.

New concepts: 'typical strong Mpemba effect' and 'typical relaxation time'.

Abstract

Relaxation in open quantum systems is fundamental to quantum science and technologies. Yet, the influence of the initial state on relaxation remains a central, largely unanswered question. Here, by systematically characterizing the relaxation behavior of generic initial states, we uncover a typicality phenomenon in high-dimensional open quantum systems: relaxation becomes nearly initial-state-independent as system size increases under verifiable conditions. Crucially, we prove this typicality for thermalization processes above a size-independent temperature. Our findings extend the typicality to open quantum dynamics, in turn identifying a class of systems where two widely used quantities -- the Liouvillian gap and the maximal relaxation time -- merit re-examination. We formalize this with two new concepts: the 'typical strong Mpemba effect' and the 'typical relaxation time'. Beyond these conceptual advances, our results provide practical implications: a scalable route to accelerating relaxation and a typical mixing-time benchmark that complements conventional worst-case metrics for quantum simulations and state preparation.