Multiqubit symmetric states with high geometric entanglement

TL;DR

This paper investigates the geometric entanglement of symmetric multiqubit states, identifying states with higher entanglement than previously known and analyzing their asymptotic behavior for large numbers of qubits.

Contribution

It introduces new symmetric states with higher geometric entanglement and derives an upper bound, advancing understanding of entanglement in symmetric multiqubit systems.

Findings

Symmetric states with higher geometric entanglement than Dicke states

Asymptotic entanglement behavior improves with new states

Derived an upper bound for the geometric measure of symmetric states

Abstract

We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement behaves asymptotically for large N. We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously. We also derive an upper bound for the geometric measure of entanglement of symmetric states. The connection with the quantumness of a state is discussed.