Reflected Entropy in AdS$_3$/WCFT

TL;DR

This paper investigates reflected entropy within the AdS$_3$/WCFT framework, establishing its holographic dual as a minimal distance in the entanglement wedge, and extends the understanding of quantum information measures in holography.

Contribution

It generalizes the computation of reflected entropy and related measures in holographic WCFT by analyzing twist operators and their charges, linking them to geometric quantities.

Findings

Reflected entropy relates holographically to the minimal distance between swing surfaces.

Computed scaling dimensions and charges of twist operators in non-Abelian orbifold WCFT.

Established a geometric interpretation of reflected entropy in holographic WCFT.

Abstract

Reflected entropy is a newly proposed notion in quantum information. It has important implications in holography. In this work, we study the reflected entropy in the framework of the AdS$_3$/WCFT correspondence. We determine the scaling dimensions and charges of various twist operators in non-Abelian orbifold WCFT by generalizing the uniformization map and taking into account of the charge conservation. This allows us to compute the reflected entropy, logarithmic negativity and odd entropy for two disjoint intervals in holographic WCFT. We find that the reflected entropy can be related holographically to the pre-entanglement wedge cross-section, which is given by the minimal distance between the benches in two swing surfaces.