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

By Stephen D. Bartlett, Terry Rudolph, Robert W. Spekkens. 2011

144 citations recorded by the source corpus.

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 mechanics with an epistemic restriction. The particular epistemic restriction we posit as our foundational postulate specifies two constraints. The first constraint is a classical analogue of Heisenberg's uncertainty principle -- the second-order moments of position and momentum defined by the phase-space distribution that characterizes an agent's knowledge are required to satisfy the same constraints as are satisfied by the moments of position and momentum observables for a quantum state. The second constraint is that the distribution should have maximal entropy for the given moments. Starting from this postulate, we derive the allowed preparations, measurements and transformations and demonstrate that they are isomorphic to those allowed in Gaussian quantum mechanics and generate the same experimental statistics. We argue that this reconstruction of Gaussian quantum mechanics constitutes additional evidence in favour of a research program wherein quantum states are interpreted as states of incomplete knowledge, and that the phenomena that do not arise in Gaussian quantum mechanics provide the best clues for how one might reconstruct the full quantum theory.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4f9fe900200d8697aa83d1706d74cc7017897c06

How researchers see this paper

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In Atomic and Molecular Physics, and Optics

1. Roger Colbeck
2. Matthew S. Leifer
3. Klaas Landsman
4. Terry Rudolph
5. Renato Renner
6. Adrian Kent

In Statistical and Nonlinear Physics

1. Matthew S. Leifer
2. Roger Colbeck
3. Klaas Landsman
4. Terry Rudolph
5. Renato Renner

Citations in the corpus

• Is the Quantum State Real? An Extended Review of -ontology Theorems (2014, background): “First of all, Spekkens’ toy theory has been generalized to larger dimensions [65] and to continuous variable systems [66].”