Question about the "reality of the quantum state" paper by Pusey, Barrettm and Rudolp In the paper I mentioned in the title (on arXiv and supposedly subsequently published in a journal), the authors claim to show that "if a quantum state merely represents information about a system, then experimental predictions are obtained which contradict those of quantum theory." When they get slightly more precise they appear to equate this high level statement to the following. If the (real) state of the system corresponds to more than one quantum state, then operators (observables) exist in which the probability of measuring any value is 0 (it's impossible to get any result from some measurements). I must have missed something, because if the latter is really what they are trying to say, then it seems to me that (1) it is not at all equivalent to the first statement and (2) the second statement isn't saying much. Don't we already know that any two quantum states are different, and hence cannot correspond to the same (real) state of the system. I.e. isn't there already some kind of theorem or something which says the Hilbert space is not redundant (except for the scalar multiples of a state) (with enough measurements of the right kind we can distinguish psi_0 from psi_1)? If the Hilbert space is not redundant then of course there cannot be a "real state" which corresponds to more than one quantum state (if it did the "real state" would be less precise than the quantum state and hence not what we would call "real"). So I think I have misunderstood their argument somehow. It seems like a useful proof would be to show that only one "real state" can be associated with a given quantum state (NOT that only one quantum state can be associated with a real state). As another question, what is the latest/best information/papers to read to understand any progress on the former problem (showing that only one real state can be associated with a given quantum state).