Classical Statistical Mechanics Approach to Multipartite Entanglement

TL;DR

This paper models multipartite entanglement in qubit systems using a statistical mechanics framework, analyzing the distribution of bipartite purity to identify maximally entangled states and revealing frustration effects.

Contribution

It introduces a novel statistical mechanics approach to characterize and optimize multipartite entanglement in qubit systems.

Findings

Distribution of bipartite purity analyzed over balanced bipartitions

Identifies frustration in the optimization landscape

Provides moments of the purity distribution at high temperature

Abstract

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.