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arXiv · 1803.11414

Equivalence determination of unitary operations

Atsushi Shimbo·Akihito Soeda·Mio Murao
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Abstract

We study equivalence determination of unitary operations, a task analogous to quantum state discrimination. The candidate states are replaced by unitary operations given as a quantum sample, i.e., a black-box device implementing a candidate unitary operation, and the discrimination target becomes another black-box. The task is an instance of higher-order quantum computation with the black-boxes as input. The optimal error probability is calculated by semidefinite programs. Arbitrary quantum operations applied between the black-boxes in a general protocol provide advantages over protocols restricted to parallelized use of the black-boxes. We provide a numerical proof of such an advantage. In contrast, a parallelized scheme is analytically shown to exhibit the optimal performance of general schemes for a particular number of quantum samples of the candidates. We find examples of finite-sample equivalence determination that achieve the same performance as when a classical description of the candidates are provided, although an exact classical description cannot be obtained from finite quantum samples.

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Atsushi Shimbo, Akihito Soeda, Mio Murao. 2018-03-30. Equivalence determination of unitary operations. https://arxiv.org/abs/1803.11414

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