Unambiguous state discrimination: optimal solution and case study

TL;DR

This paper provides a comprehensive analysis of unambiguous discrimination between two mixed quantum states, deriving optimality conditions, classifying measurements by rank, and solving the problem completely for low-dimensional cases, with practical applications.

Contribution

It introduces a general framework for optimal unambiguous state discrimination, including classification of measurements and complete solutions in low dimensions, along with a case study on quantum state comparison.

Findings

Derived operational optimality conditions for unambiguous discrimination.

Classified optimal measurements based on their rank.

Provided a complete solution for Hilbert spaces up to dimension five.

Abstract

We present a generic study of unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space dimensions smaller or equal to five this leads to the complete optimal solution. We demonstrate our method with a physical example, namely the unambiguous comparison of n quantum states, and find the optimal success probability.