Correlation and Information‐Theoretic Approaches in Quantum Coupled Double‐Well Systems

Abstract This study investigates the quantum correlation and information‐theoretic measures of coupled double‐well systems, modeled using Razavy's hyperbolic potential. By employing numerical techniques, including the finite difference method and Kronecker tensor product, the time‐independent equation is solved to determine energy eigenvalues and eigenfunctions for quantum states, such as , , , and of the bipartite quantum system. The analysis focuses on quantum information measures, such as Shannon entropy, mutual information, and statistical correlation coefficients, to understand how potential parameters and and the coupling strength influence correlations. The results reveal intricate dependencies between quantum states, highlighting symmetry and asymmetry in correlation measures for mixed states under opposite coupling potentials. Further, the different behaviors of the statistical correlation coefficients are found in position and momentum space and their information‐theoretic measures as functions of potential parameters, which is very helpful for understanding the dynamics of quantum particles in the coupled system. Additionally, the study investigates the entanglement properties of bipartite quantum states, employing von Neumann, and linear entropy to measure quantum correlations. The results provide critical insights into the dynamics of quantum particles in confined systems, connecting quantum mechanics and information theory. This work opens new avenues to exploring quantum information dynamics in Razavy double‐well systems, which gives novel insights into the role of spatial and momentum correlations in particle interactions.