Dynamical purification and the emergence of quantum state designs from the projected ensemble

Understand

Quantum thermalization in a many-body system is defined by the approach of local subsystems towards a universal form, describable as an ensemble of quantum states wherein observables acquire thermal expectation values.

• Recently, it was demonstrated that the distribution of these quantum states can also exhibit universal statistics, upon associating each state with the outcome of a local projective measurement of the complementary subsystem.
• Specifically, this collection of pure quantum states -- called the projected ensemble -- can under certain conditions mimic the behavior of a maximally entropic, uniformly random ensemble, i.e., form a {\it quantum state-design}, representing a ``deeper'' form of quantum thermalization.
• In this work, we investigate the dynamical process underlying this novel emergent universality.