Islands for Reflected Entropy

TL;DR

This paper introduces a new covariant formula for reflected entropy that accounts for entanglement islands, derived from gravitational path integrals, and demonstrates its consistency and relevance in understanding complex multipartite entanglement.

Contribution

It proposes a novel formula for reflected entropy incorporating entanglement islands, derived from generalized replica wormholes in the gravitational path integral.

Findings

The formula satisfies all necessary inequalities for reflected entropy.

It reveals multipartite entanglement structures invisible to traditional entropies.

Demonstrates the importance of islands in reflected entropy calculations.

Abstract

Recent work has demonstrated the need to include contributions from entanglement islands when computing the entanglement entropy in QFT states coupled to regions of semiclassical gravity. We propose a new formula for the reflected entropy that includes additional contributions from such islands. We derive this formula from the gravitational path integral by finding additional saddles that include generalized replica wormholes. We also demonstrate that our covariant formula satisfies all the inequalities required of the reflected entropy. We use this formula in various examples that demonstrate its relevance in illustrating the structure of multipartite entanglement that are invisible to the entropies.