Title:

Stochastic inputoutput systems in spacetime and the many facets of locality

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 Belltype 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 inputoutput systems in
spacetime, a quantum experiment may be considered as a blackbox 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 Belltype are considered within this
framework. For such stochastic inputoutput 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 Belltype experiment, the
corresponding Belltype inequalities are in fact the facetdefining inequalities of a
polytope which is given as the convex hull of a finite set of local deterministic
systems. This is the Bellpolytope, which, in general, has many facets. Using
BellTest, a computer program which we designed for the analysis of such
experiments, we find the Belltype inequalities for ideal and realistic Belltype
experiments which have outputs excluded in the ideal setup.
