Abstract In this article, we apply a statistical model for forecasting the quantum entanglement between a two‐qubit and optical field in binomial distribution. We explore the link between the atomic Fisher information, quantum entropy, and the statistical properties of the field. The qubit‐qubit entanglement is investigated through concurrence during the interaction time. The dynamics of the statistical quantities will be forecasted using the time series and neural network models. The effect of the field distribution parameter (number of successes) is examined by the time series models and artificial neural network. We compare the accuracy of both modes from the perspective of the dynamic of the quantum entropy and atomic Fisher information. A statistical description for the data has been obtained and is discussed to show the statistical technique analysis the data of statistical quantities. The results obtained have several applications and are related with quantum statistics and quantum information processing.
Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for parameter estimation and sensing. Here we introduce Fisher information as an operational metric to assess the metrological content of structured optical fields. By treating the measured intensity distribution as a statistical object, we define Fisher information with respect to physically relevant parameters, such as transverse displacement. We demonstrate that optical modes with comparable Shannon entropy can exhibit markedly different Fisher information, revealing sensitivity features associated with nodal structure and local curvature. Using Hermite--Gaussian modes as minimal test cases, we show that increasing modal order systematically enhances Fisher information. We then extend the analysis to two widely used families in structured light: Laguerre--Gaussian vortex beams and finite-energy Bessel--Gauss beams. Across these representative families, Fisher information provides a unified and experimentally accessible criterion for comparing structured optical fields in sensing applications.
We investigate the quantum-information properties of a particle confined by the double Morse potential in position and momentum spaces. The quasi-exact solvability of the model gives analytical expressions for the first two bound states, allowing the corresponding probability densities to be analyzed directly. Shannon entropy, Onicescu energy, Fisher information, statistical complexity, and Fisher-Shannon products are evaluated as functions of the parameter
A, which controls the transition from a well-separated double well to a merged single-well profile. The position distribution is more delocalized and structurally complex when the double-well character is pronounced, whereas the momentum distribution exhibits the complementary trend. As the wells merge, the ground-state Fisher--Shannon product approaches its Gaussian reference value, whereas the excited state retains stronger non-Gaussian structure.