Optimal measurement strategies for the trine states with arbitrary prior probabilities

TL;DR

This paper derives the optimal measurement strategies for discriminating trine qubit states with arbitrary prior probabilities, providing analytical solutions for minimum-error and maximum confidence strategies, advancing quantum state discrimination theory.

Contribution

It presents the second known closed-form analytical solution for minimum-error measurement strategies for trine states with arbitrary priors, expanding the understanding of quantum state discrimination.

Findings

Derived the minimum-error measurement strategy for trine states with arbitrary priors.

Provided the maximum confidence measurement strategy for the same states.

Extended analytical solutions beyond symmetric cases in quantum state discrimination.

Abstract

We investigate the optimal measurement strategy for state discrimination of the trine ensemble of qubit states prepared with arbitrary prior probabilities. Our approach generates the minimum achievable probability of error and also the maximum confidence strategy. Although various cases with symmetry have been considered and solution techniques put forward in the literature, to our knowledge this is only the second such closed form, analytical, arbitrary prior, example available for the minimum-error figure of merit, after the simplest and well-known two-state example.