Entanglement and fidelity in hydrogen electron–proton spins amid magnetic fields and decoherence

Abstract

We explore the time evolution of entanglement and fidelity in the electron–proton spin system of a hydrogen atom under the influence of external magnetic fields and Markovian dephasing noise. The hydrogen atom serves as a paradigmatic two-qubit system, in which hyperfine coupling generates intrinsic spin correlations, modulated by Zeeman splitting, which introduces field-dependent energy shifts and controls spin evolution. We consider the open-system dynamics using the Lindblad equation, incorporating local dephasing processes arising from magnetic-field fluctuations that act independently on the electron and proton spins while preserving population probabilities. Bipartite quantum correlations are quantified via the concurrence and Uhlmann fidelity, which measures the overlap between evolving states and reference preparations. Our analysis elucidates the interplay among hyperfine interactions, Zeeman effects, and environmental decoherence, revealing regimes where entanglement decays rapidly due to noise sensitivity, in contrast to greater resilience in fidelity measures. Time-dependent behaviors highlight field-induced enhancements or suppressions of correlations.