Conference Paper

# Oblivious Transfer and Quantum Channels

Group of Applied Physics, University of Geneva, 10, rue de l'École-de-Médecine, CH-1211 Genève 4, Switzerland. E-mail: ;

DOI: 10.1109/ITW.2006.1633774 Conference: Information Theory Workshop, 2006. ITW '06 Punta del Este. IEEE Source: IEEE Xplore

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**ABSTRACT:**One of the most intriguing features of quantum physics is the non-locality of correlations that can be obtained by measuring entangled particles. Recently, it has been noticed that non-locality can be studied without reference to the Hilbert space formalism. I review here the properties of the basic mathematical tool used for such studies, the so called Popescu-Rohrlich-box, in short PR-box. Among its feats, are the simulation of the correlations of the singlet and of other non-local probability distributions. Among its features, the "anomaly of non-locality" and a great power for information-theoretical tasks. Among its failures, the impossibility of reproducing all multi-partite distributions and the triviality of the allowed dynamics. Comment: Proceedings of the Conference "On the Present Status of Quantum Mechanics", Losinj, September 2005; and Festschrift for the 70th birthday of GianCarlo Ghirardi03/2006; -
##### Article: An anomaly of non-locality.

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**ABSTRACT:**Ever since the work of Bell, it has been known that entangled quantum states can rise non-local correlations. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones. Surprisingly it is not the case: non-maximally entangled states are generally more non-local than maximally entangled states for all the measures of non-locality proposed to date: Bell inequalities, the Kullback-Leibler distance, entanglement simulation with communication or with non-local boxes, the detection loophole and efficiency of cryptography. In fact, one can even find simple examples in low dimensions, confirming that it is not an artefact of a specifically constructed Hilbert space or topology. This anomaly shows that entanglement and non-locality are not only different concepts, but also truly different resources. We review the present knowledge on this anomaly, point out that Hardy's theorem has the same feature, and discuss the perspectives opened by these discoveries.Quantum Information & Computation. 01/2007; 7:157-170. -
##### Article: An anomaly of non-locality

[Show abstract] [Hide abstract]

**ABSTRACT:**Ever since the work of Bell, it has been known that entangled quantum states can rise non-local correlations. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones. Surprisingly it is not the case: non-maximally entangled states are generally more non-local than maximally entangled states for all the measures of non-locality proposed to date: Bell inequalities, the Kullback-Leibler distance, entanglement simulation with communication or with non-local boxes, the detection loophole and efficiency of cryptography. In fact, one can even find simple examples in low dimensions, confirming that it is not an artefact of a specifically constructed Hilbert space or topology. This anomaly shows that entanglement and non-locality are not only different concepts, but also truly different resources. We review the present knowledge on this anomaly, point out that Hardy's theorem has the same feature, and discuss the perspectives opened by these discoveries.Quantum information & computation 01/2006; 7(1). · 1.63 Impact Factor

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