Magnetic Control of Quantum Correlations in a Two-Qubit Spin System Under Dephasing

We investigate the time evolution of bipartite quantum correlations in the ground-state hyperfine manifold of the hydrogen atom subjected to an external magnetic field and independent Markovian dephasing. Treating the electron–proton spin pair as an effective two-qubit system, we derive the exact solution of the Lindblad master equation for an X-shaped initial state and quantify the dynamics using three complementary measures: entanglement of formation (through concurrence), quantum steering (through the CJWR inequality) and Bell nonlocality (through normalized CHSH violation). The dynamics are obtained within a unified open-system framework that combines hyperfine interaction, Zeeman splitting, and Markovian dissipation in a single analytically solvable Lindblad model, allowing a complete operator-level characterization of the correlation decay. This exact treatment provides a transparent link between the underlying spectral structure of the Hamiltonian and the observed hierarchy in the robustness of quantum correlations. Our results reveal that all three quantities exhibit damped oscillations whose frequency and decay rate are strongly tuned by the proton magnetic parameter through the Zeeman splitting. While entanglement decays relatively quickly, steering persists noticeably longer and Bell nonlocality proves to be the most fragile, confirming the expected hierarchy of quantum correlations under local dephasing. The external magnetic field emerges as a practical control knob that can extend the lifetime of these resources even in the presence of noise. These findings provide a clear physical picture of how hyperfine coupling, Zeeman effects, and environmental fluctuations jointly govern quantum coherence in atomic spin systems, with direct implications for spin-based quantum technologies and fundamental tests of nonlocality in realistic laboratory settings.