Characterizing Locally Indistinguishable Orthogonal Product States
Yuan Feng, Yaoyun Shi · IEEE Transactions on Information Theory · 2009
Bennett [PhysicalReviewA, vol. 59, no. 2, p. 1070, 1999] identified a set of orthogonal product states in the Hilbert space\BBC3otimes\BBC3such 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\BBC3otimes\BBC3and\BBC2otimes\BBC2otimes\BBC2. 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.