Is a system's wave function in one-to-one correspondence with its elements of reality?

Question

Referee this paper: arXiv:1111.6597 by Roger Colbeck, Renato Renner

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Abstract: Although quantum mechanics is one of our most successful physical theories, there has been a long-standing debate about the interpretation of the wave function---the central object of the theory. Two prominent views are that (i) it corresponds to an element of reality, i.e. an objective attribute that exists before measurement, and (ii) it is a subjective state of knowledge about some underlying reality. A recent result [Pusey et al. arXiv:1111.3328] has placed the subjective interpretation into doubt, showing that it would contradict certain physically plausible assumptions, in particular that multiple systems can be prepared such that their elements of reality are uncorrelated. Here we show, based only on the assumption that measurement settings can be chosen freely, that a system's wave function is in one-to-one correspondence with its elements of reality. This also eliminates the possibility that it can be interpreted subjectively.

Comments

By treating the wave function as a random variable (which has for each particle a definite value), the authors effectively assume already their conclusion, that the wave function is an element of reality (i.e., its components serve as hidden variables).