Islands and mixed states in closed universes

TL;DR

This paper explores how entanglement with non-gravitating systems can induce mixed states in closed universes, using braneworld models in multiboundary wormhole geometries to analyze entropy bounds and state purity.

Contribution

It introduces a model with multiple non-gravitating components to study mixed states and entropy bounds in closed universes with gravity, extending previous single-system analyses.

Findings

Entanglement can produce mixed states in closed universes with gravity.

The entropy of these mixed states is bounded by half the coarse-grained entropy.

Braneworld configurations can be fully contained or split among non-gravitating systems.

Abstract

We investigate the appearance of islands when a closed universe with gravity is entangled with a non-gravitating quantum system. We use braneworlds in three-dimensional multiboundary wormhole geometries as a model to explore what happens when the non-gravitating system has several components. The braneworld can be either completely contained in the entanglement wedge of one of the non-gravitating systems or split between them. In the former case, entanglement with the other system leads to a mixed state in the closed universe, unlike in simpler setups with a single quantum system, where the closed universe was necessarily in a pure state. We show that the entropy of this mixed state is bounded by half of the coarse-grained entropy of the effective theory on the braneworld.