Alan Sherry: Statistical Mechanics of Projected Ensembles of Mixed States

Projected ensembles—defined as ensembles of pure states on a subsystem conditioned on measurement outcomes on its complement—provide probes of quantum information beyond the reduced density matrix. This perspective has enabled a refined notion of quantum equilibration in the form of deep thermalisation, wherein projected ensembles dynamically approach universal maximum-entropy ensembles in closed quantum systems. In this talk, I will introduce a distinct paradigm of deep thermalisation for mixed states, which differs qualitatively from the pure-state case. In this formulation, the deep thermal ensemble arises by tracing out auxiliary degrees of freedom from a maximum-entropy ensemble defined on an augmented system, with the resulting ensemble structure depending explicitly on the entropy of the initial state. I will demonstrate that such ensembles emerge dynamically in generic, locally interacting chaotic spin chains. I will then show how the statistical mechanics of mixed-state projected ensembles constrains their role as probes of information scrambling, leading to measurement-invisible quantum correlations (MIQC)—an emergent phenomenon in which extensive multipartite entanglement coexists with vanishing measurement influence between subsystems. Finally, I will discuss future directions that leverage mixed-state deep thermalisation to develop finer probes of quantum information, including access to correlations in replicated Hilbert spaces that are inaccessible to conventional correlation functions.