Quantum foundations minus probability theory

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Researchers in quantum foundations claim (D'Ariano, Fuchs, ...):

Quantum = probability theory + x

and hence:

x = Quantum - probability theory

Guided by the metaphorical analogy:

probability theory / x = flesh / bones

we introduce a notion of quantum measurement within x, which, when flesing it with Hilbert spaces, provides orthodox quantum mechanical probability calculus.