Mixed-state entanglement and information recovery in thermalized states and evaporating black holes

Journal Article · Fri Jan 13 00:00:00 EST 2023 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2023)064· OSTI ID:1909621

Vardhan, Shreya ^[1]; Kudler-Flam, Jonah  ^[2]; Shapourian, Hassan ^[3]; Liu, Hong ^[1]

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1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2. Univ. of Chicago, IL (United States)
3. Microsoft Station Q, Santa Barbara, CA (United States)

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.

• Research Organization: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0012567; SC0020360
• OSTI ID: 1909621
• Journal Information: Journal of High Energy Physics (Online), Vol. 2023, Issue 1; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

Related Subjects

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