Global entanglement and coherent states in an N-partite system

TL;DR

This paper characterizes global entanglement in symmetric N-partite quantum systems, showing that only coherent states are unentangled in the symmetric subspace, while all orthogonal states are entangled.

Contribution

It provides a complete characterization of entanglement in symmetric subspaces of N-partite quKit systems, linking coherence with lack of entanglement.

Findings

Pure states in symmetric subspace are unentangled iff they are coherent states.

All states orthogonal to the symmetric subspace are globally entangled.

The results apply to systems with arbitrary local dimension K.

Abstract

We consider a quantum system consisting of N parts, each of which is a "quKit" described by a K dimensional Hilbert space. We prove that in the symmetric subspace, S, a pure state is not globally entangled, if and only if it is a coherent state. It is also shown that in the orthogonal complement all states are globally entangled.