Structural approach to unambiguous discrimination of two mixed quantum states

TL;DR

This paper investigates the optimal unambiguous discrimination between two mixed quantum states, providing a unique measurement solution, simplified conditions, and practical examples for states with rank at most 2.

Contribution

It introduces a unique optimal measurement for discriminating two mixed states, simplifies optimality conditions, and offers solutions for states with rank up to 2.

Findings

Optimal measurement is unique for two mixed states.

Simplified optimality conditions for measurement design.

Explicit solutions for states with rank at most 2.

Abstract

We analyze the optimal unambiguous discrimination of two arbitrary mixed quantum states. We show that the optimal measurement is unique and we present this optimal measurement for the case where the rank of the density operator of one of the states is at most 2 ("solution in 4 dimensions"). The solution is illustrated by some examples. The optimality conditions proved by Eldar et al. [Phys. Rev. A 69, 062318 (2004)] are simplified to an operational form. As an application we present optimality conditions for the measurement, when only one of the two states is detected. The current status of optimal unambiguous state discrimination is summarized via a general strategy.