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Quantum Knowledge in Phase Space.

Davi Geiger1

  • 1Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.

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Summary
This summary is machine-generated.

This study applies Bayesian statistics to quantum physics, treating probability as subjective belief. It introduces phase space probability density and Kullback-Liebler divergence to define quantum entanglement and interference.

Keywords:
Bayesian statisticsKullback–Liebler divergenceentanglemententropyinterference

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Area of Science:

  • Quantum Physics
  • Statistical Mechanics
  • Information Theory

Background:

  • Quantum mechanics traditionally uses objective probability.
  • Bayesian statistics offers a subjective interpretation of probability as belief.
  • Phase space representations are valuable for quantum systems.

Purpose of the Study:

  • To derive quantum probability density functions in phase space using Bayesian methods.
  • To define quantum interference and entanglement via Kullback-Liebler divergence in phase space.
  • To compare these measures with entropy and extend to mixed states.

Main Methods:

  • Bayesian derivation of probability density function in phase space.
  • Introduction of Kullback-Liebler divergence in phase space.
  • Comparative analysis with entropy.
  • Application to spin systems and mixed states.

Main Results:

  • A novel Bayesian framework for quantum probability in phase space.
  • Kullback-Liebler divergence effectively quantifies entanglement and interference.
  • Phase space entanglement is demonstrated for spin and mixed states.

Conclusions:

  • Bayesian interpretation provides a consistent framework for quantum probability.
  • Phase space divergence offers a powerful tool for analyzing quantum phenomena like entanglement.
  • The approach is extendable to more complex quantum systems.