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arXiv:quant-ph/0509123 · International Journal of Quantum Information

ENTANGLEMENT-ASSISTED ORIENTATION IN SPACE

Časlav Brukner, Nikola Paunković, Terry Rudolph, Vlatko Vedral

Published Apr 1, 2006• 21 citations
arXivHTMLPDF

Abstract

We demonstrate that quantum entanglement can help separated individuals in making decisions if their goal is to find each other in the absence of any communication between them. We derive a Bell-like inequality that the efficiency of every classical solution for our problem has to obey, and demonstrate its violation by the quantum efficiency. This proves that no classical strategy can be more efficient than the quantum one.

DOI
10.1142/s0219749906001839

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We demonstrate that quantum entanglement can help separated individuals in making decisions if their goal is to find each other in the absence of any communication between them. We derive a Bell-like inequality that the efficiency of every classical solution for our problem has to obey, and demonstrate its violation by the quantum efficiency. This proves that no classical strategy can be more efficient than the quantum one.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.
Significance For many communication complexity problems the quantum strategies, distinguished by using Bell nonlocal correlations, provide exponential advantage over the best possible classical strategies. Conversely, for any Bell nonlocal correlations there exists a communication complexity problem that is solved more efficiently using the former. Despite many efforts, there were only two problems for which one could certify that any strategy that outperforms the classical one must harbor Bell nonlocal correlations. We prove that any large advantage over the best known classical strategy makes use of Bell nonlocal correlations. Thus, we provide the missing link to the fundamental equivalence between Bell nonlocality and quantum advantage.