Structural perspectives from quantum states and measurements in optimal state discrimination

Quantum state discrimination refers to a class of techniques to identify a specific quantum state through a positive operator-valued measure . In this work, we investigate how structural information can influence our ability to determine or bound the optimal discrimination probability. First, as background, we note that for single-qubit pure-state ensembles, pairwise fidelities determine the optimal discrimination probability, whereas in higher dimensions they do not in general. As an illustrative application of this observation, we give a closed-form fidelity-based reformulation of the optimal discrimination probability for three equiprobable single-qubit states with equal pairwise fidelities. Secondly, we show that the information of measurement operators that vanish in the optimal solution can be used to refine upper bounds on the optimal discrimination probability, often yielding tighter bounds.