  We introduce the notion of a leak for general process theories, and identify
quantum theory as a theory with minimal leakage, while classical theory has
maximal leakage. We provide a construction that adjoins leaks to theories, an
instance of which describes the emergence of classical theory by adjoining
decoherence-leaks to quantum theory. Finally, we show that defining a notion of
purity for processes in general process theories has to make reference to the
leaks of that theory ---a feature missing in standard definitions--- hence, we
propose a refined definition and study the resulting notion of purity for
quantum, classical and intermediate theories.
