Distinguishability of the symmetric states

TL;DR

This paper investigates the distinguishability of symmetric multipartite quantum states within the symmetric subspace, deriving optimal measurement strategies for pure and certain mixed states, and comparing global and separable measurement approaches.

Contribution

It introduces methods to determine optimal measurements for symmetric quantum states, including separable measurements, extending previous results to more general cases.

Findings

Optimal probability and measurements for pure states derived

Separable measurements can match global measurement performance

Results applicable to linearly dependent states

Abstract

In this paper, the distinguishability of multipartite geometrically uniform quantum states obtained from a single reference state is studied in the symmetric subspace. We specially focus our attention on the unitary transformation in a way that the produced states remain in the symmetric subspace, so rotation group with Jy as the generator of rotation is applied. The optimal probability and measurements are obtained for the pure and some special mixed separable states and the results are compared with those obtained at the previous articles for the special cases. The results are valid for lin- early dependent states. The discrimination of these states is also investigated using the separable measurement. We introduce appropriate transformation to gain the optimal separable measurements equivalent to the optimal global measurements with the same optimal probability.