ABSTRACT
It is known that there are many sets of orthogonal product states which cannot be distinguished perfectly by local operations and classical communication (LOCC). However, these discussions have left the following open question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In m â n, certain classes of unextendible product bases (UPB) which can be distinguished perfectly using entanglement as a resource, had been presented in 2008. In this paper, we present protocols which use entanglement more efficiently than teleportation to distinguish some classes of orthogonal product states in m â n, which are not UPB. For the open question, our results offer rather general insight into why entanglement is useful for such tasks, and present a better understanding of the relationship between entanglement and nonlocality.
ABSTRACT
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.