Information Geometry of Quantum Entangled Gaussian Wave-Packets

Abstract

Describing and understanding the essence of quantum entanglement and its connection to dynamical chaos is of great scientific interest. In this work, using information geometric (IG) techniques, we investigate the effects of micro-correlations on the evolution of maximal probability paths on statistical manifolds induced by systems whose microscopic degrees of freedom are Gaussian distributed. We use the statistical manifolds associated with correlated and non-correlated Gaussians to model the scattering induced quantum entanglement of two spinless, structureless, non-relativistic particles, the latter represented by minimum uncertainty Gaussian wave-packets. Knowing that the degree of entanglement is quantified by the purity P of the system, we express the purity for s-wave scattering in terms of the micro-correlation coefficient r - a quantity that parameterizes the correlated microscopic degrees of freedom of the system; thus establishing a connection between entanglement and micro-correlations. Moreover, the correlation coefficient r is readily expressed in terms of physical quantities involved in the scattering, the precise form of which is obtained via our IG approach. It is found that the entanglement duration can be controlled by the initial momentum p_{o}, momentum spread σ_{o} and r. Furthermore, we obtain exact expressions for the IG analogue of standard indicators of chaos such as the sectional curvatures, Jacobi field intensities and the Lyapunov exponents. We then present an analytical estimate of the information geometric entropy (IGE); a suitable measure that quantifies the complexity of geodesic paths on curved manifolds. Finally, we present concluding remarks addressing the usefulness of an IG characterization of both entanglement and complexity in quantum physics.

37 pages, 3 figures

References in corpus (18)

• Transverse Entanglement Migration in Hilbert Space
• Entropic Dynamics
• Jacobi Fields on Statistical Manifolds of Negative Curvature
• How complex is the quantum motion?
• Works on an information geometrodynamical approach to chaos
• The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models
• Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?
• Quantifying The Complexity Of Geodesic Paths On Curved Statistical Manifolds Through Information Geometric Entropies and Jacobi Fields
• Hypersensitivity and chaos signatures in the quantum baker's maps
• Entanglement generation via scattering of two particles with hard-core repulsion
• Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature
• Information Geometry, Inference Methods and Chaotic Energy Levels Statistics
• Entanglement Generation in the Scattering of One-Dimensional Particles
• Information Geometric Modeling of Scattering Induced Quantum Entanglement
• Standard forms and entanglement engineering of multimode Gaussian states under local operations
• On The Complexity Of Statistical Models Admitting Correlations
• Kolmogorov-Sinai entropy and black holes
• Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference

Cited by in corpus (10)

• Information geometric methods for complexity
• Geometric Algebra and Information Geometry for Quantum Computational Software
• Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes
• Maximum Caliber Inference and the Stochastic Ising Model
• Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds
• Theoretical investigations of an information geometric approach to complexity
• Local softening of information geometric indicators of chaos in statistical modeling in the presence of quantum-like considerations
• Information Geometric Complexity of Entropic Motion on Curved Statistical Manifolds under Different Metrizations of Probability Spaces
• Fisher metric from relative entropy group
• Hermite-Gaussian model for quantum states