Does the quantum state ultimately represent some objective aspect of reality, or is it a way of characterizing something about us, namely, something about what some person knows about reality? This question stretches back to the earliest history of quantum theory, but has recently become an active topic again, inspiring a slew of new theoretical results and even some experimental tests.
Another reason to think the quantum state is epistemic is that, in most cases, there is no way of telling, with a single experiment, what the quantum state actually was before the experiment.
According to epistemic approaches to quantum theory, the reason you cannot experimentally distinguish most quantum states is just like the die game: There are some possibilities for the actual physical situation that are compatible with multiple quantum states.
Spekkens’s toy theory was exciting because just like in quantum theory, its states were generally “Indistinguishable”-and that indistinguishability was fully explained by their mutual compatibility with the same underlying physical situations.
Since the indistinguishability of quantum states has, for those inclined to an epistemic approach, no accepted explanation-the question is whether they can come up with one at all-Spekkens and others took this as strong evidence that quantum states might be epistemic, too, if only the toy theory could extend to more complicated systems.
The authors even proposed experiments that could tell the difference between the predictions of quantum theory and the predictions that any epistemic approach would have to make-and so far, the experiments that have been performed all agree with the standard quantum theory.
In other words, it seems you can’t interpret the quantum state as epistemic because any theory in which the state is epistemic makes predictions different from quantum theory.