I don’t understand your point 1. Are you comparing with the situation in classical mechanics, where the composite system being in a pure state implies that the reduced states are also pure? I think this is just a defect of classical mechanics, because you can’t start with a system AB about which you know everything, let B be the information you are going to ignore, and end up with a probability distribution over the states in A. If you want to described a situation of limited knowledge in classical mechanics, you have to introduce the lack of knowledge by hand, from outside the theory. There’s no mechanism in the theory to represent it.

About your point 2, no, purification does not imply that the universe is in a pure state. It merely implies that if it is in a mixed state, it must be one that can be purified (the purification in this case would be a merely mathematical device, not corresponding to an actual physical system). In any case, I agree that purification is much more natural if the universe *is* in a pure state. Well, but it is. Mixed states are not fundamental objects, but derived ones, precisely for the purpose of dealing with situations of limited knowledge.

Regarding fiducial measurements, you are missing the point. The question is precisely whether there is a finite set.

]]>The way I see it, the possible issues of purification are:

1) the idea of having maximal information about the whole but non-maximal information about the parts does not seem intuitive, which can be said to be one of the mystery of QM (aka. entanglement). This is the thing to be explained, not to be imposed by hand.

2) it implies the entire universe is a pure state, if QM is applicable to the universe as a whole. But this may be in conflict with the operational view of QM that these reconstructions of QM are taking. Taking measurements as primitive implicitly assume an external observer.

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Regarding the existence of fiducial measurements (I wonder why the papers do not use this standard term), my idea is isn’t it always true? One can always take all the possible measurement outcomes to begin with, then remove the redundant ones. There is no guarantee it will be finite though. ]]>