Quantum fidelity of symmetric multipartite states

TL;DR

This paper investigates the maximal overlap of symmetric multipartite quantum states under local operations, proving that for unitary transformations the same operation suffices, but not for more general invertible operations.

Contribution

It establishes that for symmetric multiqubit states, the optimal local unitary operation can be identical across parties, while highlighting limitations for invertible operations.

Findings

Same local unitary applied everywhere achieves maximal overlap.

Counterexamples show different operations are needed for invertible transformations.

Results clarify conditions for optimal local operations on symmetric states.

Abstract

For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each party. We show that for two symmetric multiqubit states and local unitary transformations this is the case; the maximal overlap can be reached by applying the same unitary matrix everywhere. For local invertible operations (stochastic local operations assisted by classical communication equivalence), however, we present counterexamples, demonstrating that considering the same operation everywhere is not enough.