Quantum Nonlocality without Entanglement
Abstract
We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles which also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.
Cite
@article{arxiv.quant-ph/9804053,
title = {Quantum Nonlocality without Entanglement},
author = {Charles H. Bennett and David P. DiVincenzo and Christopher A. Fuchs and Tal Mor and Eric Rains and Peter W. Shor and John A. Smolin and William K. Wootters},
journal= {arXiv preprint arXiv:quant-ph/9804053},
year = {2009}
}
Comments
27 pages, Latex, 6 ps figures. To be submitted to Phys. Rev. A. Version 2: 30 pages, many small revisions and extensions, author added. Version 3: Proof in Appendix D corrected, many small changes; final version for Phys. Rev. A Version 4: Report of Popescu conjecture modified