  Quantum simulations of Bell inequality violations are numerically obtained
using probabilistic phase space methods, namely the positive P-representation.
In this approach the moments of quantum observables are evaluated as moments of
variables that have values outside the normal eigenvalue range. There is thus a
parallel with quantum weak measurements and weak values. Nevertheless, the
representation is exactly equivalent to quantum mechanics. A number of states
violating Bell inequalities are sampled, demonstrating that these quantum
paradoxes can be treated with probabilistic methods. We treat quantum dynamics
by simulating the time evolution of the Bell state formed via parametric
down-conversion, and discuss multi-mode generalizations.
