Characterizing Locally Indistinguishable Orthogonal Product States

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 ldquo...

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Bibliographic Details
Published in:	IEEE transactions on information theory 2009-06, Vol.55 (6), p.2799-2806
Main Authors:	Feng, Yuan, Shi, Yaoyun
Format:	Article
Language:	eng
Subjects:	Applied sciences BBC Computation Computer science Euclidean space Exact sciences and technology Hilbert space Hyperrectangular representation Information technology Information theory Information, signal and communications theory Intelligent systems Laboratories locally distinguishability nonlocality without entanglement Protocols Quantum computing Quantum entanglement Quantum theory Statistics Systems engineering and theory Telecommunications and information theory
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Summary:	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.
ISSN:	0018-9448 1557-9654