Quantum predictions arising from epistemically restricted classical predictions

William F. Braasch, William K. Wootters

Published Jul 6, 2021• 0 citations

Abstract

Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is noncontextual. In this paper we start with a theory resembling Spekkens's model: we imagine a classical observer describing an experiment in terms of discrete phase space, and for each aspect of the experiment -- the state preparation, the transformations, and the measurement -- there is an epistemic restriction limiting the form of the probability distribution the classical observer may use. We show that for a certain class of systems, one can obtain the correct quantum mechanical prediction for the experiment by combining the (typically weaker) predictions of all the conceivable classical observers. The rule for effecting this combination is highly nonclassical: the ``nonrandom part of the quantum prediction is obtained by summing the ``nonrandom parts of the classical predictions.

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