Entanglement between two gravitating universes

Abstract

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the $n^{\text{th}}$ Rényi entropy includes a wormhole between the $n$ copies of the gravitating universe, leading to a standard "island formula" for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with $2n$ boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by ${\mathbb{Z}}_n$ replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a "swap wormhole", a geometry in which the boundaries of the two universes are glued together by a "swaperator". This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes -- a realization of the ER=EPR idea. The new wormhole restores unitarity of quantum information.

39 pages, 11 figures

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Cited by in corpus (10)

• Islands in Kaluza-Klein black holes
• Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
• Submerging islands through thermalization
• Islands with Gravitating Baths: Towards ER = EPR
• Page Curve of Effective Hawking Radiation
• Islands in Multiverse Models
• Entanglement between two evaporating black holes
• A comment on a fine-grained description of evaporating black holes with baby universes
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Holographic moving mirrors