Initial-State Typicality in Quantum Relaxation

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 many thermalization processes above a size-independent temperature. Our findings extend the typicality to transient 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.