Nonlocality and Contextuality: Concepts and Applications in Quantum Information

Abstract

In quantum foundations and quantum information, understanding the notion of non-cfc.ss/enfi/y is of extreme importance. This term broadly characterizes quantum phenomena which not only appear to be at odds with certain instances of classical intuition, but are provably in contradiction with empirical predic- tions of classical theories. The archetypal examples of non-classical phenomena, produced by operational quantum mechanics, are nonlocality and contextuality, which have traditionally been characterized within a framework of impossibility results, known as no-go results. Nonlocality and contextuality, while being at the core of the weirdness and conceptual issues of quantum theory, also provide useful information theoretical resources that can be harnessed for information processing purposes, for instance, in quantum computation and quantum cryp- tography. In this thesis, we detail various types of non-classical phenomena, in particular nonlocality and contextuality, by studying them within the framework of cooperation multiplayer games. This framework provides an intuitive way to interpret such no-po results as interactive protocols where agents try to jointly compute a desired function under a set of operational restrictions. Therein, the non-classical behaviour particular to the setup emerges as a resource for appropriately constructed games, powering the so called gunntutn-over-cla.ssiral advantage — a term which succinctly describes that players exploiting the full range of operational quantum strategies perform better at the game than the players restricted to the alternative classical theories. Finally, we will discuss some applications in quantum information, namely, within quantum cryptogra- phy, where different types of non-classical behaviour are of crucial importance in order to guarantee security of various protocols.