2021/05/31 by Jinzhao Wang
Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Black hole information paradox #Black hole thermodynamics #Computer science #Cosmology and Gravitation Theories #Entropy (arrow of time) #Equipartition theorem #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum entanglement #Quantum gravity #Quantum mechanics #Theoretical physics #hep-th #quant-ph
paper · pdf · doi:10.22331/q-2022-02-16-655
published as Quantum 6, 655 (2022) · 53+9 pages, many figures. v2:Section 6 added to demonstrate a refined Page curve. v3: Section 5 added to address higher Renyi entropies with a theorem; the method and its presumptions are clarified in section 3. v4: The theorem in Section 5 is replaced by a weaker version. v5: published version with the presentation revised and the proof of theorem 1 simplified
arxiv created 2022/02/14 · openalex publication_date 2022/02/16 · arxiv updated 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Rényi 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.