• Open Access

Bound Entanglement in Thermalized States and Black Hole Radiation

Shreya Vardhan, Jonah Kudler-Flam, Hassan Shapourian, and Hong Liu
Phys. Rev. Lett. 129, 061602 – Published 4 August 2022
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Abstract

We study the mixed-state entanglement structure of chaotic quantum many-body systems at late times using the recently developed equilibrium approximation. A rich entanglement phase diagram emerges when we generalize this technique to evaluate the logarithmic negativity for various universality classes of macroscopically thermalized states. Unlike in the infinite-temperature case, when we impose energy constraints at finite temperature, the phase diagrams for the logarithmic negativity and the mutual information become distinct. In particular, we identify a regime where the negativity is extensive but the mutual information is subextensive, indicating a large amount of bound entanglement. When applied to evaporating black holes, these results imply that there is quantum entanglement within the Hawking radiation long before the Page time, although this entanglement may not be distillable into Einstein-Podolsky-Rosen pairs. We claim that at this earlier time, rather than the Page time, information about diaries thrown into the black hole first starts to leak out.

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  • Received 22 March 2022
  • Accepted 15 July 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.061602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsQuantum Information, Science & Technology

Authors & Affiliations

Shreya Vardhan1,*, Jonah Kudler-Flam2,*, Hassan Shapourian3, and Hong Liu1

  • 1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
  • 3Microsoft Station Q, Santa Barbara, California 93109, USA

  • *These authors contributed equally to this work.

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Vol. 129, Iss. 6 — 5 August 2022

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