Investigation of Quantum Entanglement in Stochastic Partial Differential Equations through the Lens of Dynamical Chaos Theory

Abstract

Stochastic quantum entanglements give a basic problem in the dynamics of the coherence effect and the randomness of the dynamics. The paper examines the entanglement evolution in stochastic partial differential equations (SPDEs) in terms of dynamical chaos theory. We solve a family of SPDEs modeling quantum systems under Gaussian and Lévy noise, both in the weak and strong coupling limits. Spectral spatial discretization and stochastic Runge-Kutta time integration allow the calculation of numerically accurate solutions and the reconstruction of density matrices and calculation of entanglement measures, such as von Neumann entropy and concurrence. Measurement of chaotic properties is done by maximal Lyapunov exponents, Poincaré-type diagnostics, and sensitivity to initial conditions measures of high-dimensional stochastic dynamics. Findings indicate that stochastic forcing is much more efficient to promote entanglement and weak noise spin-offs non-zero concurrence in more than 65 percent of realizations, and high-noise regimes increase von Neumann entropy means more than 200 percent compared to deterministic baselines. Entanglement amplification is strongly related to positive Lyapunov exponents (Γ≈0.58), and high-chaos flows have oscillatory entanglement with peak-to-peak variations of 45%. Such results define a quantitative correlation between stochastic chaos and quantum correlations, and it is possible to note that the noise-induced instabilities can serve as a constructive mechanism creation of entanglements. The work gives a solid framework for studying quantum systems with stochastic perturbations and has insight that is applicable in quantum information processing, complex network dynamics, and semiclassical quantum-chaotic systems.