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Science China Physics Mechanics and Astronomy

Local discrimination scheme for some unitary operations

Tian-Qing Cao, Fei Gao, Guojing Tian, Shu-Cui Xie, Qiaoyan Wen

Published Jul 25, 2016• 5 citations
Publisher
DOI
10.1007/s11433-016-0121-8

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Scientific Reports•May 25, 2016•7 citations
Local distinguishability of bipartite unitary operations has recently received much attention. A nontrivial and interesting question concerning this subject is whether there is a sequential scheme for locally discriminating between two bipartite unitary operations, because a sequential scheme usually represents the most economic strategy for discrimination. An affirmative answer to this question was given in the literature, however with two limitations: (i) the unitary operations to be discriminated were limited to act on $d\ensuremath{\bigotimes}d$, i.e., a two-qudit system, and (ii) the inverses of the unitary operations were assumed to be accessible, although this assumption may be unrealizable in experiment. In this paper, we improve the result by removing the two limitations. Specifically, we show that any two bipartite unitary operations acting on ${d}_{A}\ensuremath{\bigotimes}{d}_{B}$ can be locally discriminated by a sequential scheme, without using the inverses of the unitary operations. Therefore, this paper enhances the applicability and feasibility of the sequential scheme for locally discriminating unitary operations.
It has been shown that any two different multipartite unitary operations are perfectly distinguishable by local operations and classical communication with a finite number of runs. Meanwhile, two open questions were left. One is how to determine the minimal number of runs needed for the local discrimination, and the other is whether a perfect local discrimination can be achieved by merely a sequential scheme. In this paper, we answer the two questions for some unitary operations U1 and U2 with locally unitary equivalent to a diagonal unitary matrix in a product basis. Specifically, we give the minimal number of runs needed for the local discrimination, which is the same with that needed for the global discrimination. In this sense, the local operation works the same with the global one. Moreover, when adding the local property to U1 or U2, we present that the perfect local discrimination can be also realized by merely a sequential scheme with the minimal number of runs. Both results contribute to saving the resources used for the discrimination.