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A Classical Formulation of Quantum Theory?

William F Braasch1, William K Wootters2

  • 1Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA.

Entropy (Basel, Switzerland)
|January 21, 2022
PubMed
Summary
This summary is machine-generated.

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This study reformulates quantum theory using classical probability distributions and phase space, not Hilbert space. Quantum theory emerges from combining multiple restricted classical viewpoints, with a characterization method shown for a single qubit.

Area of Science:

  • Quantum mechanics
  • Foundations of physics
  • Classical mechanics

Background:

  • Traditional quantum theory formulation relies on Hilbert space and quasiprobabilities.
  • Spekkens' model offers an epistemically restricted classical framework.
  • Reconciling quantum and classical descriptions remains a fundamental challenge.

Purpose of the Study:

  • To reformulate quantum theory in classical terms using phase space and actual probability distributions.
  • To develop a method for characterizing collections of restricted classical pictures.
  • To demonstrate the approach for a single-qubit system.

Main Methods:

  • Utilizing phase space instead of Hilbert space as the foundational element.
  • Employing actual probability distributions rather than quasiprobabilities.
Keywords:
Wigner functionepistemic restrictionphase spacequantum reconstructionquasiprobabilityqubit

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  • Combining multiple epistemically restricted classical models.

    • Main Results:

    • A novel reformulation of quantum theory from classical principles is presented.
    • A method for characterizing allowed sets of classical pictures is proposed.
    • The framework is successfully applied to the single-qubit case.

    Conclusions:

    • Quantum theory can be understood as a composite of restricted classical theories.
    • The proposed characterization method provides a pathway for further development.
    • This approach offers new insights into the quantum-classical relationship.