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 R\'enyi relative entropy, sandwiched R\'enyi 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.
Highlights
AND SUMMARY OF RESULTSA unifying idea spanning quantum information theory, quantum chaos and thermalization, and black hole physics is that ofdistinguishability of quantum states
Even so, using semiclassical calculations, Hawking showed that all black holes with identical thermodynamic quantities will radiate thermal radiation [2]
This means that at late times, after the black hole has evaporated, all of these microstates are completely indistinguishable, which is in sharp tension with the unitarity of quantum mechanics
Summary
A unifying idea spanning quantum information theory, quantum chaos and thermalization, and black hole physics is that of (in)distinguishability of quantum states. Even so, using semiclassical calculations, Hawking showed that all black holes with identical thermodynamic quantities (mass, charge, and angular momentum) will radiate thermal radiation [2] This means that at late times, after the black hole has evaporated, all of these microstates are completely indistinguishable, which is in sharp tension with the unitarity of quantum mechanics. This occurs in special states called “fixed-area states” [9,10] With this realization, we characterize the distinguishability of black hole microstates in anti–de Sitter (AdS) space or, equivalently, high-energy states in conformal field theories (CFTs). We characterize the distinguishability of black hole microstates in anti–de Sitter (AdS) space or, equivalently, high-energy states in conformal field theories (CFTs) We subsequently apply this formalism to a toy model of an evaporating black hole [11]. We highlight alternative derivations using free probability theory in Appendix A
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.