A canonical purification for the entanglement wedge cross-section

A canonical purification for the entanglement wedge cross-section

Blog Article

Abstract 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 chervo jacke herren 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 coq-clear 100 ubiquinol 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.