Black box correlations: locality, noncontextuality, and convex polytopes

Abstract

This dissertation studies nonlocal/contextual correlations and its generalisation from a device independent approach, where statistical data are themselves the object of study. For this, we explore a black box framework, in which a list of input buttons can be pressed to provide, with some probabilities, a list of outputs. In this formalism, we discuss general examples, analyse correlations that arise from quantum mechanics, and present all the inequalities characterise the noncontextual polytope for the n-cycle scenario. Moreover, we prove some efficiency requirements for nonlocality in an imperfect scenario, and use these results to propose a physical loophole free Bell test in an optical quantum system where photodetection and homodyne measurements are performed. Our findings contributes to the comprehension of nonlocal/contextual correlations and add to efforts towards feasible proposals for loophole-free Bell tests.