In defense of the epistemic view of quantum states: a toy theory - Rob Spekkens

What would it be like to live in a world where observers were faced with a fundamental restriction on how much knowledge they could acquire about the states of systems around them? I attempt to answer this question in a particularly simple context, where an observer's knowledge is characterized by a number of yes/no questions, and where the restriction on knowledge has a particularly simple form: the number of questions that are answered is always less than or equal to the number of questions that are unanswered. Remarkably, given a few other assumptions about this toy universe, one obtains a richly structured theory that qualitatively reproduces a wide variety of quantum phenomena. Such phenomena include the non-commutativity of measurements, the impossibility of discriminating non-orthogonal states, interference, various features of entanglement, the no cloning theorem, quantum teleportation, and many others. The quality and diversity of these analogies provides compelling evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.