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Optimal Information Transfer and the Uniform Measure over Probability Space.

Entropy (Basel, Switzerland)·2023
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A Classical Interpretation of the Scrooge Distribution.

William K Wootters1

  • 1Department of Physics, Williams College, Williamstown, MA 01267, USA.

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This study provides a classical interpretation for the quantum mechanical Scrooge distribution. Researchers found a natural classical explanation for its real-amplitude version, offering insights into quantum mechanics and classical probability.

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GAP measureaccessible informationsubentropy

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Area of Science:

  • Quantum Mechanics
  • Probability Theory
  • Information Theory

Background:

  • The Scrooge distribution is a quantum mechanical concept.
  • It is a probability distribution over pure states, minimizing information leakage upon measurement.
  • Previously, it lacked a natural classical interpretation.

Purpose of the Study:

  • To offer a classical interpretation of the Scrooge distribution.
  • To explore the relationship between quantum mechanics and classical probability theory.

Main Methods:

  • Considered a real-amplitude version of the Scrooge distribution.
  • Analyzed the transition to the complex-amplitude case.

Main Results:

  • A non-trivial, natural classical interpretation was found for the real-amplitude Scrooge distribution.
  • The transition to the complex-amplitude case presented challenges but offered insights.

Conclusions:

  • The Scrooge distribution can be interpreted classically, particularly in its real-amplitude form.
  • This work illuminates the connections between quantum and classical probability frameworks.