A classical formulation of quantum theory?

TL;DR

This paper investigates reformulating quantum theory using classical phase space with restricted probability distributions, aiming to understand quantum phenomena through classical models, exemplified by the single qubit case.

Contribution

It proposes a new approach to derive quantum theory from classical phase space models with epistemic restrictions, focusing on characterizing allowed classical pictures.

Findings

Successfully applied the approach to a single qubit.

Provided a method to characterize classical pictures compatible with quantum theory.

Demonstrated how classical models can reproduce quantum features.

Abstract

We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model introduced by Spekkens. We obtain quantum theory only by combining a collection of restricted classical pictures. Our main challenge in this paper is to find a simple way of characterizing the allowed sets of classical pictures. We present one promising approach to this problem and show how it works out for the case of a single qubit.