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

• Published in: Entropy (Basel, Switzerland) Vol. 26; no. 3; p. 263
• Main Authors: Edrisi, Arash, Patwa, Hamza, Morales Escalante, Jose A.
• Format: Journal Article
• Language: English
• 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
• DOI: 10.3390/e26030263
• ISSN: 1099-4300

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.