Detecting and Preserving Quantum Steering in Hydrogen Atoms: Entropic Inequalities and Lindblad Dynamics

In the present work, we investigate the detection and control of quantum correlations in the hyperfine structure of hydrogen atoms under dissipative dynamics. The hydrogen atom serves as a fundamental platform for studying bipartite quantum correlations between the electron and proton spins, where entanglement is quantified by concurrence and EPR steering is witnessed through violation of the entropic steering inequality. By modeling the open-system evolution via the Lindblad master equation, we analyze the time-dependent behavior of concurrence, steering, and fidelity under varying dissipation rates. Numerical illustrations highlight the resilience of entanglement relative to steering in noisy environments, providing insights into the control of non-classical phenomena.