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Entropy and wigner functions

Manfredi1, Feix

  • 1Laboratoire de Physique des Milieux Ionises, Universite Henri Poincare, BP239, 54506 Vandoeuvre-les-Nancy, France.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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This study introduces a new quantum entropy definition using Wigner functions, which naturally quantifies quantum entanglement. Smoothing Wigner functions increases entropy, aiding in constructing valid probability distributions.

Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Mathematical physics

Background:

  • The Wigner function provides a phase-space representation of quantum states.
  • Quantifying entanglement is crucial for understanding quantum systems.
  • Existing entropy measures may not fully capture properties relevant to Wigner representations.

Purpose of the Study:

  • To define and explore an alternative measure of quantum entropy based on Wigner functions.
  • To demonstrate the utility of this Wigner-based entropy in quantifying quantum entanglement.
  • To establish a connection between Wigner function smoothing and entropy changes.

Main Methods:

  • Utilizing the Wigner representation of quantum mechanics.
  • Developing a novel definition of quantum entropy derived from Wigner functions.

Related Experiment Videos

  • Analyzing the effect of smoothing operations on Wigner functions and associated entropy.
  • Deriving rules for constructing admissible Wigner functions and positive-definite probability distributions.

    • Main Results:

    • An alternative definition of quantum entropy based on Wigner functions is proposed.
    • This Wigner-based entropy measure effectively quantifies the entanglement of quantum states.
    • Smoothing of the Wigner function demonstrably leads to an increase in the defined entropy.
    • A method for constructing positive-definite probability distributions that are also admissible Wigner functions is derived.

    Conclusions:

    • The Wigner function representation offers a natural framework for defining quantum entropy.
    • The proposed entropy measure provides a valuable tool for entanglement quantification.
    • The relationship between Wigner function smoothing and entropy provides insights into quantum state properties.