Coherent states and global entanglement in an N qubit system

TL;DR

This paper characterizes the relationship between coherent states and global entanglement in symmetric N-qubit systems, showing that symmetric coherent states are not entangled while orthogonal states are always entangled.

Contribution

It establishes a clear criterion linking coherent states to the absence of global entanglement in symmetric subspaces of N-qubit systems.

Findings

Symmetric coherent states are not globally entangled.

States orthogonal to symmetric subspace are always globally entangled.

Provides a characterization of entanglement in symmetric N-qubit systems.

Abstract

We consider an $N$ qubit system and show that in the symmetric subspace, $\mathbb{S}$ a state is not globally entangled, iff it is a coherent state. It is also proven that in the orthogonal complement $\mathbb{S}_{\bot}$ all states are globally entangled.