A Numerical Study of Quantum Entropy and Information in the Wigner–Fokker–Planck Equation for Open Quantum Systems

Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase space desc...

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Bibliographic Details
Published inEntropy (Basel, Switzerland) Vol. 26; no. 3; p. 263
Main Authors Edrisi, Arash, Patwa, Hamza, Morales Escalante, Jose A.
Format Journal Article
LanguageEnglish
Published Switzerland MDPI AG 14.03.2024
MDPI
Subjects
Analysis
Applied mathematics
Energy levels (Quantum mechanics)
Entropy
Entropy (Information theory)
Euler–Maruyama
Fokker-Planck equation
Friction
Information science
Initial conditions
Kinetic theory
Mathematical functions
Methods
Monte Carlo
Numerical analysis
open quantum systems
Quantum computing
quantum information
System design
Systems analysis
Wigner–Fokker–Planck
United States
Husimi transform
quantum entropy
Monte Carlo
Wehrl entropy
open quantum systems
Wigner–Fokker–Planck
Euler–Maruyama
kinetic theory
quantum information
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Summary:Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase space description. We perform a numerical inspection of the Wehrl entropy for the benchmark problem of a harmonic potential, since the existence of a steady state and its analytical formula have been proven theoretically in this case. When there is friction in the noise terms, no theoretical results on the monotonicity of absolute entropy are available. We provide numerical results of the time evolution of the entropy in the case with friction using a stochastic (Euler–Maruyama-based Monte Carlo) numerical solver. For all the chosen initial conditions studied (all of them Gaussian states), up to the inherent numerical error of the method, one cannot disregard the possibility of monotonic behavior even in the case under study, where the noise includes friction terms.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e26030263