Abstract
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 Schrődinger 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 {mathcal {H}}_text{A} to each systemtext{A}; (2) compose two systems by the tensor product rule {mathcal {H}}_{text{A}text{B}}={mathcal {H}}_text{A}otimes {mathcal {H}}_text{B}; (3) associate a transformation from system text{A} to text{B} to a quantum operation, i.e. to a completely positive trace-non-increasing map between the trace-class operators of text{A} and text{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.
Highlights
We all have become accustomed to a set of rules that we call Quantum Theory (QT), which we believe must hold for the whole physical domain at the fundamental level, in a theory of gravity
In quantum gravity the Hawking radiation from black-hole posed the problem of violation of unitarity [1]. This started a debate that is still open. Is it violation of unitarity an infringement of a law of QT? As a matter of facts it is almost universally believed that in QT the two following statements hold: (1) all transformations are achieved as a unitary interaction followed by a von-Neumann measurement; (2) all mixed states are marginals of pure entangled states
Such dogma of ontology of purification originated from the von Neumann axiomatisation of QT [2], which largely relies on the Schrődinger equation as a postulate, the latter being valid in a nonrelativistic context and in free quantum field theory, but no longer in the interacting theory
Summary
We all have become accustomed to a set of rules that we call Quantum Theory (QT), which we believe must hold for the whole physical domain at the fundamental level, in a theory of gravity. As a matter of facts it is almost universally believed that in QT the two following statements hold: (1) all transformations are achieved as a unitary interaction followed by a von-Neumann measurement; (2) all mixed states are marginals of pure entangled states. Such dogma of ontology of purification originated from the von Neumann axiomatisation of QT [2], which largely relies on the Schrődinger equation as a postulate, the latter being valid in a nonrelativistic context and in free quantum field theory, but no longer in the interacting theory.. I will conclude the paper with a short discussion about the role of unitarity and state purity in the theory
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