Generalizations of Reflected Entropy and the Holographic Dual

TL;DR

This paper introduces generalized reflected entropy measures for multipartite states and demonstrates their holographic duals as minimal surface configurations, with explicit calculations confirming the duality.

Contribution

It defines new multipartite correlation measures and establishes their holographic duals as entanglement wedge cross sections, supported by large central charge computations.

Findings

Holographic duals of the new measures are various minimal surface configurations.

Large c calculations of Δ_R agree with holographic predictions.

Supports the conjecture that Δ_R is dual to multipartite entanglement wedge cross sections.

Abstract

We introduce a new class of quantum and classical correlation measures by generalizing the reflected entropy to multipartite states. We define the new measures for quantum systems in one spatial dimension. For quantum systems having gravity duals, we show that the holographic duals of these new measures are various types of minimal surfaces consist of different entanglement wedge cross sections. One special generalized reflected entropy is $\Delta_R$, with the holographic dual proportional to the so called multipartite entanglement wedge cross section $\Delta_W$ defined before. We then perform a large $c$ computation of $\Delta_R$ and find precise agreement with the holographic computation of 2$\Delta_{W}$. This agreement shows another candidate $\Delta_R$ as the dual of $\Delta_W$ and also supports our holographic conjecture of the new class of generalized reflected entropies.