Islands and Uhlmann phase: Explicit recovery of classical information from evaporating black holes

Abstract

Recent work has established a route towards the semiclassical validity of the Page curve, and so provided evidence that information escapes an evaporating black hole. However, a protocol to explicitly recover and make practical use of that information in the classical limit has not yet been given. In this paper, we describe such a protocol, showing that an observer may reconstruct the phase space of the black hole interior by measuring the Uhlmann phase of the Hawking radiation. The process of black hole formation and evaporation provides an invertible map between this phase space and the space of initial matter configurations. Thus, all classical information is explicitly recovered. We assume in this paper that replica wormholes contribute to the gravitational path integral.

30 pages, 12 figures. Added references and clarifications, to match published version. Comments highly appreciated

References in corpus (7)

• The entropy of Hawking radiation
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• Observations of Hawking radiation: the Page curve and baby universes
• Wormhole calculus, replicas, and entropies
• Operational approach to the Uhlmann holonomy
• Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry
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• Entanglement entropy in holographic moving mirror and Page curve
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• Edge modes as reference frames and boundary actions from post-selection
• Defect Extremal Surface for Reflected Entropy
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation