Initial-State Typicality in Quantum Relaxation
arXiv:2511.01709 · doi:10.1103/wgr5-lb6b
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.
Accepted by PRL. Minor revisions in Conclusion and Outlook
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- Quantum Mpemba effect in chaotic systems with conservation laws
- Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
- Ergotropic Mpemba crossings in finite-dimensional quantum batteries