A canonical purification for the entanglement wedge cross-section

Journal Article · Thu Mar 18 00:00:00 EDT 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep03(2021)178· OSTI ID:1852920

Dutta, Souvik ^[1]; Faulkner, Thomas ^[1]

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1. Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics

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.

• Research Organization: Univ. of Illinois at Urbana-Champaign, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0019183
• OSTI ID: 1852920
• Journal Information: Journal of High Energy Physics (Online), Vol. 2021, Issue 3; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics
AdS-CFT Correspondence
Conformal Field Theory
Renormalization Group