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Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality". After a brief review of Zurek's derivation it is argued that this claim is exaggerated if not wholly unjustified. In order to demonstrate that Born's rule arises noncircularly from deterministically evolving quantum states, it is not sufficient to assume that quantum states are somehow associated with probabilities and then prove that these probabilities are given by Born's rule. One has to show how irreducible probabilities can arise in the context of an ontological no-collapse interpretation of quantum states. It is argued that the reason why all attempts to do this have so far failed is that quantum states are fundamentally algorithms for computing correlations between possible measurement outcomes, rather than evolving ontological states.

The description of quantum states by probability distributions of classical-like random variables associated with observables is presented. An invertible map of the wave functions and density matrices onto the probability distributions is constructed. The relation of the probability distributions to quasidistributions like the Wigner function is discussed. The interference phenomenon and superposition principle of pure quantum states are given in the form of nonlinear addition of the probabilities identified with the quantum states. The probability given by Born’s rule is expressed as a function of the probabilities describing the system states. The suggested probability representation of quantum mechanics is presented using examples of harmonic oscillators and qubits.