  It is almost universally believed that in quantum theory the two following
statements hold: 1) all transformations are achieved by a unitary interaction
followed by a von Neumann measurement; 2) all mixed states are marginals of
pure entangled states. I name this doctrine the dogma of purification ontology.
The source of the dogma is the original von Neumann axiomatisation of the
theory, which largely relies on the Schroedinger equation as a postulate, which
holds in a nonrelativistic context, and whose operator version holds only in
free quantum field theory, but no longer in the interacting theory. In the
present paper I prove that both ontologies of unitarity and state purity are
unfalsifiable, even in principle, and therefore axiomatically spurious. I
propose instead a minimal four-postulate axiomatisation: 1) associate a Hilbert
space HA to each system A; 2) compose two systems by the tensor product rule
HAB = HAxHB; 3) associate a transformation from system A to B to a quantum
operation, i.e. to a completely positive trace-non-increasing map between the
trace-class operators of A and B; 4) (Born rule) evaluate all joint
probabilities through that of a special type of quantum operation: the state
preparation. I then conclude that quantum paradoxes-such as the
Schroedinger-cat's, and, most relevantly, the information paradox-are
originated only by the dogma of purification ontology, and they are no longer
paradoxes of the theory in the minimal formulation. For the same reason, most
interpretations of the theory (e.g. many-world, relational, Darwinism,
transactional, von Neumann-Wigner, time-symmetric, ...) interpret the same
dogma, not the strict theory stripped of the spurious postulates.
