Entanglement negativity and minimal entanglement wedge cross sections in holographic theories

By Jonah Kudler-Flam, S. Ryu. Physical Review D, 2018

166 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/af60495b0f5f1f423c27ab570b434e3048150ebd

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In Astronomy and Astrophysics

1. Joshua Sandor
2. Dominik Neuenfeld
3. I. Reyes
4. H. Chen
5. R. Myers
6. Aninda Sinha
7. Ling-Yan Hung
8. M. Smolkin

In Atomic and Molecular Physics, and Optics

1. H. Chen
2. Joshua Sandor
3. Dominik Neuenfeld
4. I. Reyes
5. R. Myers
6. T. Takayanagi
7. Shira Chapman
8. H. Marrochio

In Nuclear and High Energy Physics

1. Joshua Sandor
2. Dominik Neuenfeld
3. I. Reyes
4. H. Chen
5. R. Myers
6. Aninda Sinha
7. Ling-Yan Hung
8. M. Smolkin

Citations in the corpus

• Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, background): “In particular, there are a number of proposals relating these holographic surfaces to various entanglement measures: entanglement of purification [130, 131], reflected entropy [132], odd entanglement entropy [133–135], or entanglement negativity [136, 137].”