Characterising Locally Indistinguishable Orthogonal Product States

IEEE-Inst Electrical Electronics Engineers Inc
Publication Type:
Journal Article
IEEE Transactions On Information Theory, 2009, 55 (6), pp. 2799 - 2806
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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.
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