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

Tapas Ranjan Patra 

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. Key Words: Quantum Entropy, Groundwater Quality Assessment, Quantum Probabilistic Clustering, Hydrogeochemical Risk Zonation