A canonical purification for the entanglement wedge cross-section

By Souvik Dutta, T. Faulkner. Journal of High Energy Physics, 2019

277 citations recorded by the source corpus.

In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy. From the bulk point of view, we show that half the area of the reflected minimal surface gives a reinterpretation of the notion of the entanglement wedge cross-section. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an explicit holographic construction of the canonical purification, introduced by Engelhardt and Wall; the reflected minimal surfaces are simply RT surfaces in this new spacetime. We contrast our results with the entanglement of purification conjecture, and finally comment on the continuum limit where we find a relation to the split property: the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor introduced by Doplicher and Longo.

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

View Paper: https://www.semanticscholar.org/paper/ea4a9d83211e9f58bc47604362dd2b848e3681ec

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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].”