Wednesday, June 5, 2013

1306.0719 (Giulio Chiribella et al.)

Unitary gate discrimination with multiple queries    [PDF]

Giulio Chiribella, Giacomo Mauro D'Ariano, Martin Roetteler
We investigate the resources needed to identify an unknown unitary gate among a finite set of alternatives, considering both deterministic and probabilistic discrimination strategies. For unambiguous discrimination, where errors are not tolerated but inconclusive outcomes are allowed, we prove that parallel strategies are sufficient to identify the gate with minimum number of queries. This result is used to provide upper and lower bounds on the minimum number of queries and on the minimum ancilla dimension. In addition, we introduce the notion of generalized t- designs, which includes unitary t-designs and group representations as special cases. For gates forming a generalized t-design we prove that there is no difference between probabilistic and deterministic gate discrimination. Hence, evaluating of the query complexity of perfect discrimination is reduced to the easier problem of evaluating the query complexity of unambiguous discrimination. Finally, we consider discrimination strategies where the use of ancillas is forbidden, providing upper bounds on the number of additional queries needed to make up for the lack of ancillas.
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