# Optimal discrimination of single-qubit mixed states

## TL;DR

This paper introduces an analytical algebraic method for optimally discriminating single-qubit mixed quantum states with minimum error, applicable to any number of states and prior probabilities, complementing geometric approaches.

## Contribution

It provides a constructive, algebraic solution to the minimum-error discrimination problem for single-qubit mixed states, expanding beyond existing geometric methods.

## Key findings

- Analytical Helstrom condition-based method developed
- Applicable to any number of states and prior probabilities
- Complements geometric approaches

## Abstract

We consider the problem of minimum-error quantum state discrimination for single-qubit mixed states. We present a method which uses the Helstrom conditions constructively and analytically; this algebraic approach is complementary to existing geometric methods, and solves the problem for any number of arbitrary signal states with arbitrary prior probabilities.