Dear Miroljub,
Let me respond to each of your points in turn.
1. Mixed states are often regarded on an equal footing with pure states.
There is no problem as long as both mixed and pure states are considered pre-probabilities, i.e., they generate probability distributions on properly defined sample spaces. But one should not confuse probabilities and their referents, i.e., the events of which they are probabilities; conceptually these are two very different things in ordinary probability theory as well as in applications of probability theory in quantum mechanics. I know of no situations in quantum information/computation which require ignoring this distinction. You will find some discussion of quantum information in Sec. 7 of “A consistent quantum ontology”, Stud. Hist. Phil. Mod. Phys. 44, pp. 93-114. arXiv:1105.3932v2.
2. Mixed states are part of the formalism.
I agree, but then one should use them consistently in an appropriate way as I have indicated above. Your are proposing, or so it seems to me, something that is not appropriate.
3. I am not enthusiastic about introducing multiple times when the quantum formalism seems to work perfectly well with a single time. I see no reason to make things more complicated.
Bob Griffiths
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