# Parametric separation of symmetric pure quantum states

## TL;DR

This paper develops analytical methods for probabilistic quantum state separation of symmetric states, optimizing success probability and enabling improved quantum information protocols like teleportation.

## Contribution

It provides explicit solutions and constructions for parametric state separation of symmetric quantum states, enhancing discrimination strategies and practical implementations.

## Key findings

- Success probability is shown to be optimal.
- Explicit POVM constructions are provided.
- Improved quantum teleportation success and fidelity.

## Abstract

Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or independent quantum states. We obtained analytical solutions for the success probability of the maps--which is shown to be optimal--as well as explicit constructions in terms of positive operator valued measures. Our results can be used for state discrimination strategies interpolating continuously between minimum-error and unambiguous (or maximum-confidence) discrimination, which, in turn, have many applications in quantum information protocols. As an example, we show that quantum teleportation through a nonmaximally entangled quantum channel can be accomplished with higher probability than the one provided by unambiguous (or maximum-confidence) discrimination and with higher fidelity than the one achievable by minimum-error discrimination. Finally, an optical network is proposed for implementing parametric state separation.