Lorraine Ford
My PoV is more empirical. Nature does what it does for its own reasons, which I think of as outside Plato's cave, the precise details of which may or may not be entirely beyond my/our understanding. My/our task is nonetheless to try to predict what Nature will do next just well enough to make a useful difference to my/our well-being.
As an empiricist, I have adopted an idea that the data we have or might have (and, vitally, what we know about that data, aka 'metadata') is a starting point that might be usefully different from the usual starting point that we are measuring properties of particles etc, which can often be more misleading than helpful. Data about throws of a coin (h,h,t,h,h,t,t,t, ...) is not different in kind from Data about a beam through a Stern-Gerlach apparatus (u,u,d,u,u,d,d,d,...), but the metadata tells us what other data might be correlated with what we have gathered. We might take video of how the coin is being thrown to give us advance notice of what each new data item would be, but that's not what we would do to make better predictions about the Stern-Gerlach data.
Equally, for Schrödinger's cat(s), statistics would be about a sequence (a,a,d,a,a,d,d,d,...) and the data we would collect to better predict what the result will be might be about the internal state of the cat or other things that break the 4th wall of the play. I think a quantum state (or an equivalently more elaborate than alive/dead classical state) of the cat in the box does give us marginally more information than ordinary statistics, without actually being a look inside the box.
I think it helps to think in terms of an enhanced classical statistics that takes into account many experiments, not just the cat in a box. A quantum state tells us what the results of other measurements would be, not just whether the cat is alive or dead: we can ask what the probabilities would be for other yes/no questions, which classically might be something like "Is the cat half-dead?": that's different, even for a classical vet, from asking what the probability is that the cat is dead. One example of an abstract form of such a generalized statistics is the mathematics of Generalized Probability Theory. That's not physics, so it can be used by classical vets, physicists, ..., as much as it has been used by QM/QFT.
All that may be so much nonsense to you, but you could look at slide #37 of the PDF that is linked to in a contemporaneous post on FQxI Forums (and, for that same PDF on Dropbox, here) and at slide #7 for a relatively elementary example of how Generalized Probability Theory can be made to do useful classical work that makes it empirically as effective as QM.
