Locality in Deep Thermalisation

Projective measurements can entangle causally disconnected subregions, but the abstract says generic locally interacting systems retain emergent locality: deep thermalisation and entanglement teleportation both appear on logarithmic-in-distance timescales, except in special circuits with finite-time non-local behavior.

TL;DR — The abstract studies deep thermalisation in a subsystem split into two disjoint subregions that remain causally disconnected under unitary dynamics. It states that onset is bounded by measurement-induced entanglement teleportation. Generic locally interacting systems show logarithmic-in-distance timescales for both deep thermalisation and entanglement teleportation, while special circuits can show finite-time deep thermalisation and genuine non-locality.

Core problem

Deep thermalisation is described in the abstract as the emergence of universal quantum state ensembles on subsystems after projective measurements are made on the complement. The paper asks whether this phenomenon is local.

The locality test is set up by splitting a subsystem into two disjoint subregions that remain causally disconnected at all times under unitary dynamics. If deep thermalisation appears across those two pieces, the effect cannot be explained by ordinary unitary causal contact between them.

The abstract's central answer is that deep thermalisation in this geometry is bounded by measurement-induced entanglement teleportation between the subregions.

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