Reflected Entropy in Double Holography

TL;DR

This paper explores reflected entropy in double holography, incorporating quantum matter effects, and provides numerical results for pure AdS and black hole backgrounds, revealing the interplay between geometry and quantum contributions.

Contribution

It introduces a quantum entanglement wedge cross-section concept to account for higher-order quantum corrections in reflected entropy within doubly holographic models.

Findings

Reflected entropy includes geometric and quantum matter contributions.

Numerical results match semi-classical gravity and CFT correlation predictions.

Proportion of contributions varies with Newton constants.

Abstract

Recently, the reflected entropy is proposed in holographic approach to describe the entanglement of a bipartite quantum system in a mixed state, which is identified as the area of the reflected minimal surface inside the entanglement wedge. In this paper, we study the reflected entropy in the doubly holographic setup, which contains the degrees of freedom of quantum matter in the bulk. In this context, we propose a notion of quantum entanglement wedge cross-section, which may describe the reflected entropy with higher-order quantum corrections. We numerically compute the reflected entropy in pure AdS background and black hole background in four dimensions, respectively. In general, the reflected entropy contains the contribution from the geometry on the brane and the contribution from the CFT. We compute their proportion for different Newton constants and find that their behaviors are in agreement with the results based on the semi-classical gravity and the correlation of CFT coupled to the bath CFT.