Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

Jonah Kudler-Flam, Shinsei Ryu

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46 Scopus citations

Abstract

We calculate logarithmic negativity, a quantum entanglement measure for mixed quantum states, in quantum error-correcting codes and find it to equal the minimal cross sectional area of the entanglement wedge in holographic codes with a quantum correction term equal to the logarithmic negativity between the bulk degrees of freedom on either side of the entanglement wedge cross section. This leads us to conjecture a holographic dual for logarithmic negativity that is related to the area of a cosmic brane with tension in the entanglement wedge plus a quantum correction term. This is closely related to (though distinct from) the holographic proposal for entanglement of purification. We check this relation for various configurations of subregions in AdS3/CFT2. These are disjoint intervals at zero temperature, as well as a single interval and adjacent intervals at finite temperature. We also find this prescription to effectively characterize the thermofield double state. We discuss how a deformation of a spherical entangling region complicates calculations and speculate how to generalize to a covariant description.

Original languageEnglish (US)
Article number106014
JournalPhysical Review D
Volume99
Issue number10
DOIs
StatePublished - May 15 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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