  The underlying probabilistic theory for quantum mechanics is
non-Kolmogorovian. The order in which physical observables will be important if
they are incompatible (non-commuting). In particular, the notion of
conditioning needs to be handled with care and may not even exist in some
cases. Here we layout the quantum probabilistic formulation in terms of von
Neumann algebras, and outline conditions (non-demolition properties) under
which filtering may occur.
