Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction

@article{Bartlett2012ReconstructionOG,
  title={Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction},
  author={Stephen D. Bartlett and Terry Rudolph and Robert W. Spekkens},
  journal={Physical Review A},
  year={2012},
  volume={86}
}
How would the world appear to us if its ontology was that of classical mechanics but every agent faced a restriction on how much they could come to know about the classical state? We show that in most respects, it would appear to us as quantum. The statistical theory of classical mechanics, which specifies how probability distributions over phase space evolve under Hamiltonian evolution and under measurements, is typically called Liouville mechanics, so the theory we explore here is Liouville… 

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