Comparison protocol is optimal for quantum discrimination of single-qubit unitary gates--two candidates, one quantum sample per candidate
Akihito Soeda, Atsushi Shimbo, Mio Murao · arXiv (Cornell University) · 2021
We analyze a discrimination problem of a single-qubit unitary gate with two candidates, where the candidates are not provided with their classical description, but their quantum sample is. The target gate is chosen equally among the candidates. We obtain the optimal protocol that maximizes the expected success probability, assuming the Haar distribution for the candidates. This problem is originally introduced in Hillery et al. (J. Mod. Opt. 2010) which provides a protocol achieving 7/8 in the expected success probability based on the ``unitary protocol of Andersson et al. (J. Phys. A 2003). The optimality of the protocol has been an open question since then. We prove the optimality of the comparison protocol, implying that only one of the two samples (one for each candidate) is needed to achieve an optimal discrimination. The optimization includes protocols outside the scope of quantum testers due to the dynamic ordering of the sample and target gates within a given protocol.