  A significant part of quantum theory can be obtained from a single innovation
relative to classical theories, namely, that there is a fundamental restriction
on the sorts of statistical distributions over physical states that can be
prepared. This is termed an "epistemic restriction" because it implies a
fundamental limit on the amount of knowledge that any observer can have about
the physical state of a classical system. This article provides an overview of
epistricted theories, that is, theories that start from a classical statistical
theory and apply an epistemic restriction. We consider both continuous and
discrete degrees of freedom, and show that a particular epistemic restriction
called classical complementarity provides the beginning of a unification of all
known epistricted theories. This restriction appeals to the symplectic
structure of the underlying classical theory and consequently can be applied to
an arbitrary classical degree of freedom. As such, it can be considered as a
kind of quasi-quantization scheme; "quasi" because it generally only yields a
theory describing a subset of the preparations, transformations and
measurements allowed in the full quantum theory for that degree of freedom, and
because in some cases, such as for binary variables, it yields a theory that is
a distortion of such a subset. Finally, we propose to classify quantum
phenomena as weakly or strongly nonclassical by whether or not they can arise
in an epistricted theory.
