Multipartite entanglement in qubit systems

TL;DR

This paper introduces a measure of multipartite entanglement for n-qubit systems based on average bipartite purity, and explores the structure and maximizers of this measure, identifying states with uniform maximal bipartite entanglement.

Contribution

It proposes a new entanglement potential based on bipartition purity and characterizes the maximally entangled states with uniform bipartite entanglement across all partitions.

Findings

Maximally multipartite entangled states have bipartite entanglement independent of the bipartition.

The paper derives explicit expressions for the entanglement potential.

Examples for small numbers of qubits illustrate the properties of these states.

Abstract

We introduce a potential of multipartite entanglement for a system of n qubits, as the average over all balanced bipartitions of a bipartite entanglement measure, the purity. We study in detail its expression and look for its minimizers, the maximally multipartite entangled states. They have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. We investigate their structure and consider several examples for small n.