Multipartite Entanglement and Frustration

TL;DR

This paper explores the relationship between multipartite entanglement and frustration in quantum systems, showing how minimizing bipartition purity across many partitions reveals conflicts and links to quantum frustration.

Contribution

It introduces a novel connection between frustration and multipartite entanglement by analyzing purity across all balanced bipartitions in quantum systems.

Findings

Minimal bipartition purity can conflict across different bipartitions.

Frustration arises when trying to minimize purity for all bipartitions simultaneously.

Multipartite entanglement relates to the average purity over balanced bipartitions.

Abstract

Some features of the global entanglement of a composed quantum system can be quantified in terms of the purity of a balanced bipartition, made up of half of its subsystems. For the given bipartition, purity can always be minimized by taking a suitable (pure) state. When many bipartitions are considered, the requirement that purity be minimal for all bipartitions can engender conflicts and frustration arises. This unearths an interesting link between frustration and multipartite entanglement, defined as the average purity over all (balanced) bipartitions.