Hoban, M.J.; (2012) Computational perspectives on Bell Inequalities and many-body quantum correlations. Doctoral thesis , UCL (University College London).

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Abstract

The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems violate a Bell inequality [Bell1964]. We put forward a computational perspective on a broad class of Bell tests that study correlators, or the statistics of joint measurement outcomes. We associate particular maps, or functions to particular theories. The violation of a Bell inequality then implies the ability to perform some functions, or computations that classical, or more generally, local hidden variable (LHV) theories cannot. We derive an in�finite class of Bell inequalities that establish a link to so-called "non-local games" [Cleve2004]. We then make the connection between Raussendorf and Briegel's formulation of Measurement-based Quantum Computing (MBQC) [Raussendorf2001], and these non-local games. Not only can we show that a quantum violation implies a computational advantage in this model, we show that adaptive measurements are required to perform all quantum computations. Finally, we explore post-selection of data in Bell tests from both a practical and conceptual point-of-view, with particular consideration to so-called "loopholes". Loopholes allow LHV theories to simulate quantum correlations through post-selection. We give a computational description of how loopholes can emerge in diff�erent post-selection scenarios. This motivates us to �find a form of post-selection that does not lead to loopholes. Central again to this discussion is the description of LHV theories in terms of computations. Interestingly, quantum correlators can be made more "non-classical" with this loophole-free post-selection. This method of post-selection also can simulate information processing tasks, such as MBQC, that have time-like separated components. This opens up new avenues for the study of time-like tasks studied within the space-like separated scenario of the Bell test.

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