  Ontological theories of quantum mechanics describe a single system by means
of well-defined classical variables and attribute the quantum uncertainties to
our ignorance about the underlying reality represented by these variables. We
consider the general class of ontological theories describing a quantum system
by a set of variables with Markovian (either deterministic or stochastic)
evolution. We provide the first proof that the number of continuous variables
can not be smaller than 2N-2, N being the Hilbert space dimension. Thus, any
ontological Markovian theory of quantum mechanics requires a number of
variables which grows exponentially with the physical size. This result is
relevant also in the framework of quantum Monte Carlo methods.
