Capacity of entanglement in random pure state

TL;DR

This paper calculates the capacity of entanglement for bipartite random pure states using the replica method, providing an exact finite-dimensional expression and discussing its implications in gravitational path integrals.

Contribution

It introduces an exact formula for the capacity of entanglement in finite-dimensional bipartite random pure states and links it to gravitational path integral saddle points.

Findings

Exact expression for capacity of entanglement in finite dimensions

Capacity receives contributions only from sub-leading saddle points in gravity

Links quantum information measures to gravitational geometries

Abstract

We compute the capacity of entanglement in the bipartite random pure state model using the replica method. We find the exact expression of the capacity of entanglement which is valid for a finite dimension of the Hilbert space. We argue that in the gravitational path integral, the capacity of entanglement receives contributions only from the sub-leading saddle points corresponding to the partially connected geometries.