Optimal programmable unambiguous discriminator between two unknown latitudinal states

TL;DR

This paper derives the optimal solution and success probabilities for unambiguous discrimination between two unknown latitudinal quantum states, extending previous work on universal programmable discriminators.

Contribution

It systematically derives the optimal programmable unambiguous discriminator for latitudinal states, revealing that the optimal setting matches that of universal states.

Findings

Analytical success probabilities obtained for the discrimination.

Optimal setting for latitudinal states matches universal states.

Results applicable for laboratory implementation.

Abstract

Two unknown states can be unambiguously distinguished by a universal programmable discriminator, which has been widely discussed in previous works and the optimal solution has also been obtained. In this paper, we investigate the programmable unambiguous discriminator between two unknown "latitudinal" states, which lie in a subspace of the total state space. By equivalence of unknown pure states to known average mixed states, the optimal solution for this problem is systematically derived, and the analytical success probabilities for the optimal unambiguous discrimination are obtained. It is beyond one's expectation that the optimal setting for the programmable unambiguous discrimination between two unknown "latitudinal" states is the same as that for the universal ones. The results in this work can be used for the realization of the programmable discriminator in laboratory.