Multipartite Optimized Correlation Measures and Holography

TL;DR

This paper develops optimized multipartite correlation measures in quantum information and holography, linking these measures to geometric properties of bulk surfaces in holographic duals, thus deepening the understanding of quantum correlations.

Contribution

It introduces a systematic procedure to derive symmetric optimized correlation measures for three parties and constructs their holographic duals using bulk surface geometries.

Findings

New correlation measures vanish only on product states.

Holographic duals are constructed as linear combinations of bulk surfaces.

Geometry of surfaces encodes the symmetry and optimal purification points.

Abstract

We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities, and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and the recently introduced Q-correlation and R-correlation. Some correlation measures vanish only on product states, and thus quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.