Characterizing Locally Indistinguishable Orthogonal Product States

Abstract

Bennett [Physical Review A, vol. 59, no. 2, p. 1070, 1999] identified a set of orthogonal product states in the Hilbert space \BBC 3 otimes\BBC 3 such that reliably distinguishing those states requires nonlocal quantum operations. While more examples have been found for this counterintuitive ldquononlocality without entanglementrdquo phenomenon, a complete and computationally verifiable characterization for all such sets of states remains unknown. In this paper, we give such a characterization for both \BBC 3 otimes\BBC 3 and \BBC 2 otimes\BBC 2 otimes\BBC 2. As a consequence, we show that in both spaces, there is no additional set of a fundamentally different structure than those of the known instances.