Initial-State Typicality in Quantum Relaxation

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.

Figures (1)

• Figure 1: Variance of $a_2$ for the dissipative TFIM with different spin number $N$. The system size varies from $N=2$ to $N=9$ ($d=512$). Other parameters are $E=J=g=1.0$, $\gamma=0.5$. (a) $\beta=0.1$, high temperature (b) $\beta=100$, low temperature. Solid and dashed lines denote the analytical results obtained from Eqs. \ref{['var_Haar']} and \ref{['var_HS']}, respectively. Circle and square dots are pure numerical results obtained by random sampling $10000$ initial states from the Haar and the HS measure.