Optimized Correlation Measures in Holography

TL;DR

This paper investigates optimized correlation measures in holography, demonstrating that for certain quantum states, the optimal purification has a semi-classical geometric dual, confirming existing proposals and suggesting new techniques for holographic dual determination.

Contribution

It proves that optimized correlation measures on holographic states have semi-classical geometric duals and confirms several holographic dual proposals.

Findings

Optimal purifications have semi-classical geometric duals.

Confirmed the $n$-party squashed entanglement holographic dual.

Proposed holographic entropy inequalities and direct geometry optimization techniques.

Abstract

We consider a class of correlation measures for quantum states called optimized correlation measures, defined as a minimization of a linear combination of von Neumann entropies over purifications of a given state. Examples include the entanglement of purification $E_P$ and squashed entanglement $E_{\text{sq}}$. We show that when evaluating such measures on ``nice" holographic states in the large-$N$ limit, the optimal purification has a semi-classical geometric dual. We then apply this result to confirm several holographic dual proposals, including the $n$-party squashed entanglement. Moreover, our result suggests two new techniques for determining holographic duals: holographic entropy inequalities and direct optimization of the dual geometry.