The geometric measure of entanglement for a symmetric pure state with positive amplitudes

TL;DR

This paper proves that for symmetric pure states with non-negative amplitudes, the closest product state in terms of fidelity can be chosen as a symmetric product state, advancing understanding of entanglement measures.

Contribution

It confirms the conjecture for a specific class of symmetric states, providing a partial proof in the study of geometric entanglement measures.

Findings

The conjecture holds for symmetric pure states with non-negative amplitudes.

The general conjecture remains unresolved.

The work advances understanding of entanglement in symmetric quantum states.

Abstract

In this paper for a class of symmetric multiparty pure states we consider a conjecture related to the geometric measure of entanglement: 'for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a symmetric product state'. We show that this conjecture is true for symmetric pure states whose amplitudes are all non-negative in a computational basis. The more general conjecture is still open.