Distinguishing Random and Black Hole Microstates

Abstract

This is an expanded version of the short report [Phys. Rev. Lett. 126, 171603 (2021)], where the relative entropy was used to distinguish random states drawn from the Wishart ensemble as well as black hole microstates. In this work, we expand these ideas by computing many generalizations including the Petz Rényi relative entropy, sandwiched Rényi relative entropy, fidelities, and trace distances. These generalized quantities are able to teach us about new structures in the space of random states and black hole microstates where the von Neumann and relative entropies were insufficient. We further generalize to generic random tensor networks where new phenomena arise due to the locality in the networks. These phenomena sharpen the relationship between holographic states and random tensor networks. We discuss the implications of our results on the black hole information problem using replica wormholes, specifically the state dependence (hair) in Hawking radiation. Understanding the differences between Hawking radiation of distinct evaporating black holes is an important piece of the information problem that was not addressed by entropy calculations using the island formula. We interpret our results in the language of quantum hypothesis testing and the subsystem eigenstate thermalization hypothesis (ETH), deriving that chaotic (including holographic) systems obey subsystem ETH for all subsystems less than half the total system size.

57 pages

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Cited by in corpus (14)

• Negativity Spectra in Random Tensor Networks and Holography
• Rényi Mutual Information in Quantum Field Theory
• Defect extremal surfaces for entanglement negativity
• Quantum thermodynamics of holographic quenches and bounds on the growth of entanglement from the QNEC
• Microstructure in matrix elements
• Beyond islands: A free probabilistic approach
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Subsystem distances between quasiparticle excited states
• A comment on a fine-grained description of evaporating black holes with baby universes
• Trace distance between fermionic Gaussian states from a truncation method
• Large and Small Corrections to the JLMS Formula from Replica Wormholes
• The Holographic Map of an Evaporating Black Hole
• Subsystem Trace-Distances of Two Random States
• On Quantum Information Before the Page Time