Multipartite entanglement groups

TL;DR

This paper introduces a novel group-theoretic framework to classify and analyze multipartite entanglement in pure quantum states, revealing restrictions like monogamy and connecting to quantum tasks.

Contribution

It defines entanglement groups using stabilizer quotients, providing a new classification scheme and insights into entanglement restrictions in multi-partite systems.

Findings

Entanglement groups encode monogamy restrictions.

The classification scheme aligns with known quantum tasks.

Group theory underpins multipartite entanglement properties.

Abstract

We propose to characterize multipartite entanglement of pure states as local unitary transformations acting on some parts of a system that can be undone by local unitary transformations acting on other parts. This leads to a definition of multipartite entanglement in terms of entanglement groups, constructed as certain quotients of the stabilizer group and its subgroups. We analyze properties of these entanglement groups and show that they imply restrictions which correspond to monogamy of entanglement. We use these groups to propose a coarse-grained classification scheme for entanglement in multi-partite quantum systems and we show that this group theory characterization of entanglement underlies several well-known quantum tasks.