The refined quantum extremal surface prescription from the asymptotic
equipartition property
- URL: http://arxiv.org/abs/2105.05892v5
- Date: Mon, 14 Feb 2022 13:03:01 GMT
- Title: The refined quantum extremal surface prescription from the asymptotic
equipartition property
- Authors: Jinzhao Wang
- Abstract summary: One-shot information-theoretic entropies are more fundamental entropy measures from the quantum information perspective.
We combine the technical methods from both quantum information and quantum gravity to put this idea on firm grounds.
We derive the refined quantum extremal surface prescription for fixed-area states via a novel AEP replica trick.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Information-theoretic ideas have provided numerous insights in the progress
of fundamental physics, especially in our pursuit of quantum gravity. In
particular, the holographic entanglement entropy is a very useful tool in
studying AdS/CFT, and its efficacy is manifested in the recent black hole page
curve calculation. On the other hand, the one-shot information-theoretic
entropies, such as the smooth min/max-entropies, are less discussed in AdS/CFT.
They are however more fundamental entropy measures from the quantum information
perspective and should also play pivotal roles in holography. We combine the
technical methods from both quantum information and quantum gravity to put this
idea on firm grounds. In particular, we study the quantum extremal surface
(QES) prescription that was recently revised to highlight the significance of
one-shot entropies in characterizing the QES phase transition. Motivated by the
asymptotic equipartition property (AEP), we derive the refined quantum extremal
surface prescription for fixed-area states via a novel AEP replica trick,
demonstrating the synergy between quantum information and quantum gravity. We
further prove that, when restricted to pure bulk marginal states, such
corrections do not occur for the higher R\'enyi entropies of a boundary
subregion in fixed-area states, meaning they always have sharp QES transitions.
Our path integral derivation suggests that the refinement applies beyond
AdS/CFT, and we confirm it in a black hole toy model by showing that the Page
curve, for a black hole in a superposition of two radiation stages, receives a
large correction that is consistent with the refined QES prescription.
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