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  • Letter
  • Open Access

Entanglement of purification in random tensor networks

Chris Akers*

Thomas Faulkner† and Simon Lin‡

Pratik Rath§

  • Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801-3080, USA

  • Department of Physics, University of California, Santa Barbara, California 93106, USA

  • *cakers@mit.edu
  • †tomf@illinois.edu
  • ‡shanlin3@illinois.edu
  • §rath@ucsb.edu
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Phys. Rev. D 109, L101902 – Published 6 May, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L101902

Abstract

The entanglement of purification EP(A∶B) is a powerful correlation measure, but it is notoriously difficult to compute because it involves an optimization over all possible purifications. In this paper, we prove a new inequality: EP(A∶B)≥12SR(2)(A∶B), where SR(n)(A∶B) is the Renyi reflected entropy. Using this, we compute EP(A∶B) for a large class of random tensor networks at large bond dimension and show that it is equal to the entanglement wedge cross section EW(A∶B), proving a previous conjecture motivated from AdS/CFT.

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Outline

Information

Phys. Rev. D 109, L101902– Published 6 May, 2024
  • Received 16 August 2023
  • Accepted 8 April 2024
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