Optimal Discrimination Between Two Pure States and Dolinar-Type Coherent-State Detection

We consider the problem of discrimination between two pure quantum states. We present a unified approach which finds the optimal measurement under any distortion measure that satisfies a convexity relation with respect to the Bhattacharyya distance. The well-known results for the error probability, log-loss and 'erasure-distortion' criteria are obtained as special cases. We also treat a special setting of great practical interest, the discrimination between two coherent-light waveforms. Dolinar showed that a simple detector, with an optimal local signal, obtains the quantum-optimal error probability. By applying the convexity approach, we obtain in a unified manner the optimal local signal for the same criteria as in the general setting.