  In order to find a physical axiomatization of quantum theory, physical
theories are often considered as a special case of a much more general
framework of generalized probabilistic theories. We first present a detailed
introduction to generalized probabilistic theories before we examine new
approaches towards a physical axiomatization of quantum theory. The main result
of the thesis is that one postulate concerning post-measurement states (which
have gained almost no attention in this context so far) is sufficient to rule
out all probabilistic theories with a polytopic state space, except for
classical theory. The postulate states that a measurement with a definite
outcome does not alter the state. This rules out almost all toy theories
considered so far, for instance the PR-box, but is compatible with quantum
theory. Thus, this result can be seen as an approach towards a classification
of quantum theory in physical terms. It only deals with local state spaces, in
contrast to other approaches that are mostly concerned with nonlocality in
composite systems.
