19969 2112.00020 10.1007/JHEP01(2023)064 64 64 Mixed-state entanglement and information recovery in thermalized states and evaporating black holes 02 Physical Sciences 0206 Quantum Physics Regular Article - Theoretical Physics 1 113 2023 1 13 2022 6 7 2022 12 19 2023 1 13 The Author(s) 2023 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2023 2023 1 1 Shreya Vardhan vardhan@mit.edu Jonah Kudler-Flam jkudlerflam@uchicago.edu Hassan Shapourian hassan.shapp@gmail.com Hong Liu hong_liu@mit.edu grid.116068.8 0000 0001 2341 2786 Center for Theoretical Physics Massachusetts Institute of Technology Cambridge MA 02139 USA grid.170205.1 0000 0004 1936 7822 Kadanoff Center for Theoretical Physics University of Chicago Chicago IL 60637 USA grid.419815.0 0000 0001 2181 3404 Microsoft Station Q Santa Barbara CA 93109 USA Abstract We study the universal behavior of quantum information-theoretic quantities in thermalized isolated quantum many-body systems and evaporating black holes. In particular, we study a genuine mixed-state entanglement measure called the logarithmic negativity, other correlation measures including the Renyi negativities and the mutual information, and a signature of multipartite entanglement called the reflected entropy. We also probe the feasibility of recovering quantum information from subsystems of a thermalized quantum many-body system or from the radiation of an evaporating black hole, using quantities such as relative entropy and Petz map fidelity. A recently developed technique called the equilibrium approximation allows us to probe these quantities at finite temperature. We find striking qualitative differences from the infinite temperature case, which has been the topic of previous studies using Haar-random states. In particular, we find regimes where the logarithmic negativity is extensive but the mutual information is sub-extensive, indicating a large amount of undistillable, bound entanglement in thermalized states. For evaporating black holes at finite temperature, both the logarithmic negativity and the Petz map fidelity reveal an important new time scale t b , which is earlier than the Page time t p by a finite fraction of the total evaporation time. We find that t b , as opposed to t p , is the time scale at which quantum entanglement between different parts of the radiation becomes extensive, and the fidelity of information recovery for a large diary thrown into the black hole starts to grow. Keywords 2D Gravity AdS-CFT Correspondence Black Holes Thermal Field Theory ArXiv ePrint: 2112.00020 These authors contributed equally to the work. (Shreya Vardhan, Jonah Kudler-Flam)