Characterizing locally indistinguishable orthogonal product states

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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 of orthogonal product states in the Hilbert space ℂ3⊗ ℂ3such 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 ℂ3⊗ ℂ3and ℂ2⊗ ℂ2⊗ ℂ2. 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. © 2009 IEEE.
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