In 1964, John Bell showed that a local hidden variables model cannot accommodate all the statistical predictions of quantum theory. This incompatibility was demonstrated by way of the negation of an inequality which put bounds on the expectation values of experimental outcomes. This inequality is known as Bell's inequality, its generalizations are known as Bell-type inequalities, and a Bell or Belltype experiment is a quantum experiment that tests for the violation of such an inequality. . According to the cl)lssical theory of stochastic input-output systems in spacetime, a quantum experiment may be considered as a black-box that has input and output ports distributed along its spacetime boundary and which is at rest in the laboratory frame. For each run of an experiment there are classical input events, i, and classical output events, j, which represent the settings of the devices that determine what quantum variable is to be measured and the outcomes of a quantum measurement respectively. In this thesis, quantum experiments of the Bell-type are considered within this framework. For such stochastic input-output systems, the relation between the inputs and outputs is defined in terms of the measurable conditional probabilities !P(jli), which depend on the probabilities !PCF) of local transfer functions F We define weak nonlocality, or nonlocality in the sense of Bell, as astatistical property of the classical inputs and outputs for which it is impossible to express the conditional probabilities in terms of local transfer functions alone. At least one nonlocal transfer function may have to have nonzero probability. We show that for a given Bell-type experiment, the corresponding Bell-type inequalities are in fact the facet-defining inequalities of a polytope which is given as the convex hull of a finite set of local deterministic systems. This is the Bell-polytope, which, in general, has many facets. Using BellTest, a computer program which we designed for the analysis of such experiments, we find the Bell-type inequalities for ideal and realistic Bell-type experiments which have outputs excluded in the ideal setup.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:487751 |
| Date | January 2006 |
| Creators | Basoalto, Roberto Max |
| Publisher | Queen Mary, University of London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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