Quantum Entropy & Probabilistic Clustering for Uncertainty-Aware Groundwater Quality Assessment in Geochemically Complex Terrains of Eastern India

Groundwater quality assessment in geochemically heterogeneous regions is often constrained by deterministic models that overlook spatial variability, inter-parameter dependencies, and system uncertainty. This study proposes a novel Quantum Entropy-based Groundwater Quality Index (QEGWI), which leverages von Neumann entropy derived from quantum density matrices to weight hydrogeochemical parameters based on multivariate uncertainty dynamically. Applied to a five-year dataset from 1,280 monitoring sites across Odisha, India, QEGWI demonstrated superior sensitivity, spatial resolution, and robustness compared to conventional and Shannon entropy-based indices. Sensitivity analysis revealed fluoride (F⁻) and sodium (Na⁺) as the dominant pollutants (Sobol index > 0.35), while Monte Carlo simulations confirmed model stability (σ ± 0.14). To complement this, a Quantum Probabilistic Clustering (QPC) framework was introduced, modelling groundwater sites as quantum states and utilising fidelity-based soft classification. Five risk-based clusters were identified with high intra-cluster coherence (fidelity > 0.85) and transitional zones showing uncertainty > 0.25. Together, QEGWI and QPC offer a scalable, uncertainty-aware framework that bridges quantum information theory with environmental risk assessment for hydro geologically complex systems.