Abstract

It has been shown that for two different multipartite unitary operations U1 and U2, when tr(U1†U2) = 0, they can always be perfectly distinguished by local operations and classical communication in the single-run scenario. However, how to find the detailed scheme to complete the local discrimination is still a fascinating problem. In this paper, aiming at some U1 and U2 acting on the bipartite and tripartite space respectively, especially for U1†U2 locally unitary equivalent to the high dimensional X-type hermitian unitary matrix V with trV = 0, we put forward the explicit local distinguishing schemes in the single-run scenario.

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