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Bell's Inequalities — Foundations and Quantum Communication

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Handbook of Natural Computing

Abstract

For individual events, quantum mechanics makes only probabilistic predictions. Can one go beyond quantum mechanics in this respect? This question has been a subject of debate and research since the early days of the theory. Efforts to construct a deeper, realistic level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a hidden-variable program necessarily requires outcomes of certain experiments to disagree with the predictions of quantum theory are called “no-go theorems.” The Bell theorem excludes local hidden variable theories. The Kochen–Specker theorem excludes non-contextual hidden variable theories. In local hidden-variable theories faster-than-light-influences are forbidden, thus the results for a given measurement (actual, or just potentially possible) are independent of the settings of other measurement devices which are at space-like separation. In non-contextual hidden-variable theories, the predetermined results of a (degenerate) observable are independent of any other observables that are measured jointly with it.

It is a fundamental doctrine of quantum information science that quantum communication and quantum computation outperform their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind the better-than-classical performance of information-processing tasks. This chapter aims at establishing connections between certain quantum information protocols and foundational issues in quantum theory. After a brief discussion of the most common misinterpretations of Bell's theorem and a discussion of what its real meaning is, we will demonstrate how quantum contextuality and violation of local realism can be used as useful resources in quantum information applications. In any case, the readers should bear in mind that this chapter is not a review of the literature of the subject, but rather a quick introduction to it.

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Acknowledgments

Support from the Austrian Science Foundation FWF within Project No. P19570-N16, SFB FoQuS and CoQuS No. W1210-N16, and the European Commission, Projects QAP and QESSENCE, is acknowledged. MZ is supported by MNiSW grant N202 208538. The collaboration is a part of an ÖAD/MNiSW program.

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Authors and Affiliations

  1. Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria

    Časlav Brukner

  2. Institute of Theoretical Physics and Astrophysics, University of Gdansk, Gdańsk, Poland

    Marek Żukowski

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  1. Časlav Brukner
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  2. Marek Żukowski
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Editors and Affiliations

  1. LIACS, Leiden University, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Computer Science Department, University of Colorado, Boulder, USA

    Grzegorz Rozenberg

  3. LIACS, Leiden University, Leiden, The Netherlands

    Thomas Bäck

  4. LIACS, Leiden University, Leiden, The Netherlands

    Joost N. Kok

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Brukner, Č., Żukowski, M. (2012). Bell's Inequalities — Foundations and Quantum Communication. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_42

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