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Computational perspectives on Bell Inequalities and many-body quantum correlations

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

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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 infinite 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 different 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.

Type:Thesis (Doctoral)
Title:Computational perspectives on Bell Inequalities and many-body quantum correlations
Open access status:An open access version is available from UCL Discovery
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Physics and Astronomy

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