A quantum prediction as a collection of epistemically restricted classical predictions

A toy model due to Spekkens is constructed by applying an epistemic restriction to a classical theory but reproduces a host of phenomena that appear in quantum theory. The model advances the position that the quantum state may be interpreted as a reflection of an agent’s knowledge. However, the model fails to capture all quantum phenomena because it is non-contextual. Here we show how a theory similar to the one Spekkens proposes requires only a single augmentation to give quantum theory for certain systems. Specifically, one must combine all possible epistemically restricted classical accounts of a quantum experiment. The rule for combination is simple: sum the nonrandom parts of all classical predictions to arrive at the nonrandom part of the quantum prediction.