Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence determination of unitary operations   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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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph