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Continuous input nonlocal games

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Abstract

We present a family of nonlocal games in which the inputs the players receive are continuous. We study three representative members of the family. For the first two a team sharing quantum correlations (entanglement) has an advantage over any team restricted to classical correlations. We conjecture that this is true for the third member of the family as well.

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Notes

  1. To be more precise, each of the quadrants corresponds to the truth table of the a < b or a > b formulation of the first game.

  2. The differential of a solid angle, \(\Upomega\), in spherical coordinates is proportional to \(\sin\theta\). This introduces a weight function when integrating over θ and \(\varphi\).

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Acknowledgments

We acknowledge support from the Israeli Science Foundation (Grants No. 784/06 and 990/06), and from the European Commission under the Integrated Project Qubit Applications (QAP) funded by the IST Directorate (Contract No. 015848).

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Author notes

  1. Jonathan Silman

    Present address: Laboratoire d’Information Quantique, Université Libre de Bruxelles (ULB), 1050, Bruxelles, Belgium

  2. Shai Machnes

    Present address: Institut für Theoretische Physik, Universität Ulm, Albert Einstein Allee 11, 89081, Ulm, Germany

Authors and Affiliations

  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Netanel Aharon, Shai Machnes, Benni Reznik, Jonathan Silman & Lev Vaidman

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  1. Netanel Aharon
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  2. Shai Machnes
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  3. Benni Reznik
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  4. Jonathan Silman
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  5. Lev Vaidman
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Correspondence to Netanel Aharon.

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Aharon, N., Machnes, S., Reznik, B. et al. Continuous input nonlocal games. Nat Comput 12, 5–8 (2013). https://doi.org/10.1007/s11047-012-9354-5

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  • DOI: https://doi.org/10.1007/s11047-012-9354-5

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