Abstract:
Bennett et al [Physical Review A, vol.59, no. 2, p. 1070, 1999] identified a set or orthogonal product states in the Hilbert space C-3 circle times C-3 such that reliably distinguishing those states requires nonlocal quantum operations. While more examples have been found for this counterintuitive "nonlocality without entanglement" 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 C-3 circle times C-3 and C-2 circle times C-2 circle times C-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.
