A new study explores the nature of locality in the phenomenon of deep thermalization, where universal quantum state ensembles emerge in subsystems due to projective measurements on their complement. Researchers examined a subsystem partitioned into two disjoint subregions that remain causally disconnected under unitary dynamics. The work reveals that the onset of deep thermalization in this configuration is fundamentally bounded by measurement-induced entanglement teleportation between the subregions.

Although measurements on the environment generate entanglement across the disconnected partitions, suggesting apparent non-locality, the study demonstrates that generic locally interacting systems exhibit emergent locality. Specifically, the timescales for both deep thermalization and entanglement teleportation scale logarithmically with the distance separating the subregions. This implies that, despite the quantum connection, the influence of measurements propagates in a way that respects a form of locality.

Exceptions to this rule exist, such as certain special circuits where the randomness of measurement outcomes is perfectly transmitted to the subsystem's state ensemble, conditioned on those outcomes. In these particular cases, the timescale for deep thermalization is finite, leading to genuine non-locality. This finding underscores the complexity of quantum interactions and how locality can manifest or be circumvented in different thermalization scenarios.