ar X iv : 0 90 9 . 26 11 v 1 [ qu an t - ph ] 1 4 Se p 20 09 Bell ’ s Inequalities : Foundations and Quantum Communication

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 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 hiddenvariable 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 noncontextual hidden variable theories. In local hidden-variable theories faster-thatlight-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 noncontextual 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 outperforms their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind betterthan-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 discusion of the most common misinterpretations of Bell’s theorem and a discussion of what its real me aning is, it Časlav Brukner Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna; Institute of Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna e-mail: [email protected] Marek Żukowski Institute for Theoretical Physics and Astrophysics, University of Gdansk, 80-952 Gdansk, Poland e-mail: [email protected]