  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.
