Coherence-induced deep thermalization transition

Deep thermalization refers to the emergence of universal, maximally entropic distributions of wavefunctions on a local subsystem upon conditioning on measurements of its environment. This represents a fine-grained notion of equilibration in quantum dynamics, well suited to the measurement capabilities of quantum simulators. I will present a model of quantum dynamics that exhibits a novel "deep ergodicity breaking" transition: although the system equilibrates to infinite temperature on average (i.e., at the level of reduced density matrices), the underlying wavefunction distributions sharply change from maximally entropic ("Haar ensemble", corresponding to deep thermalization) to minimally entropic ("classical bitstring ensemble") as a function of the choice of input state and measurement basis. The transition can be understood in terms of coherence---the information-theoretic resource of quantum superposition. This phenomenon represents a novel form of ergodicity breaking in quantum dynamics and opens the door to further resource-driven transitions, with potential applications in quantum information processing.