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arXiv:2606.11731 · Physica A Statistical Mechanics and its Applications

Quantum Correlation Hierarchy and Teleportation in Dephased Hydrogen Hyperfine System

Geerthana Thiyagarajan, R. Muthuganesan

quant-phSubmitted Jun 10, 2026• Announced Jun 11, 2026• 0 citations
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Abstract

We study the dynamics of quantum correlations in the hydrogen hyperfine spin system subject to Markovian phase noise. Treating the electron and proton spin degrees of freedom as an open two-qubit system governed by an isotropic hyperfine Hamiltonian and local dephasing, we obtain the exact time-dependent density matrix and derive analytical expressions for the full X-state family. We compute concurrence($C$), trace-distance measurement-induced nonlocality (Trace MIN--$\mathcal{N}_1$), and average steering coherence (ASC) in closed form and establish their strict ordering $ C(t)\leq \mathcal{N}_1(t)\leq \mathrm{ASC}(t) $ at all times. Entanglement is identified as the most fragile resource, undergoing sudden death at a finite time. Trace MIN exhibits dephasing-immune freezing for states with nonzero population imbalance, while ASC is the most robust quantity, persisting longest in every scenario studied.We additionally demonstrate that the dephased thermal hyperfine state serves as a resource for quantum teleportation, deriving a closed-form expression for the average fidelity and establishing that the teleportation advantage window coincides exactly with the entanglement survival interval, $\mathcal{F}_A > 2/3 \Longleftrightarrow \mathcal{C} > 0$, for the full X-state family with maximally mixed marginals. We identify four distinct dynamical regimes and map all three correlation measures onto directly measurable Pauli spin correlators, enabling experimental reconstruction of the full hierarchy without full state tomography.

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We investigate the quantum dynamics of entanglement and fidelity in the hyperfine structure of hydrogen atoms under dephasing noise, modeled via the Lindblad master equation. The effective Hamiltonian captures the spin–spin interaction between the electron and proton, with dephasing incorporated through local Lindblad operators. Analytical solutions for the time-dependent density matrix are derived for various initial states, including separable, partially entangled, and maximally entangled configurations. Entanglement is quantified using the concurrence, while fidelity measures the similarity between the evolving state and the initial state. Numerical results demonstrate that entanglement exhibits oscillatory decay modulated by the dephasing rate, with anti-parallel spin states displaying greater robustness compared to parallel configurations, often leading to entanglement sudden death. Fidelity dynamics reveal similar damped oscillations, underscoring the interplay between coherent hyperfine evolution and environmental dephasing. These insights elucidate strategies for preserving quantum correlations in atomic systems, with implications for quantum information processing and metrology.
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.
In this paper, we investigate the dynamics of quantum correlations in the ground-state hyperfine manifold of the hydrogen atom subjected to a static external magnetic field and local pure dephasing. The electron–proton spin pair is modeled as a bipartite two-qubit system evolving under the combined effects of hyperfine coupling, Zeeman splitting, and a Lindblad master equation that describes Markovian dissipative processes. Employing exact analytical solutions for the time-dependent density matrix elements (derived in the Markovian open-system framework), we quantify entanglement persistence via concurrence and state stability via Uhlmann fidelity with respect to the initial preparation. For an initial Werner state, numerical results reveal that the external magnetic field substantially modifies the system dynamics: Both concurrence and fidelity exhibit pronounced dependence on the Zeeman parameter, producing field-controlled oscillations, delayed entanglement sudden death, and altered decoherence rates. This behavior originates from Zeeman-induced lifting of hyperfine degeneracies, symmetry breaking of the isotropic Werner state, and redistribution of populations and coherences. Unlike previous studies that treat hyperfine interactions, Zeeman splitting, or decoherence in isolation, the present work provides a unified analytical treatment that simultaneously incorporates all three mechanisms. The findings underscore the competition between coherent hyperfine coupling and environmental noise and open new pathways for precision spectroscopy and robust quantum information protocols based on atomic spin degrees of freedom.
This work presents a comprehensive study of quantum correlations and their degradation under environmental dephasing within the atomic hydrogen system. By analyzing the magnetic coupling between the electron and proton spins in the 1s hyperfine state, we elucidate how coherent spin interactions generate entangled states and govern their temporal evolution. The investigation focuses on three key measures of quantum correlations—Bell nonlocality, Einstein–Podolsky–Rosen (EPR) steering, and quantum purity—each reflecting a different level within the hierarchy of nonclassical correlations. Analytical formulations and numerical simulations reveal that, in the absence of decay, all quantities remain steady, indicating the preservation of coherence. When dephasing is introduced, each measure decays exponentially toward a stationary lower bound, with Bell nonlocality identified as the most fragile, followed by steering and purity. A three-dimensional analysis of Werner states under dephasing further establishes the critical purity thresholds required for Bell inequality violations. The results highlight the interdependence between magnetic coupling, decoherence, and initial entanglement, providing a unified framework for understanding correlation dynamics in open quantum systems. These findings have direct implications for the development of noise-resilient quantum information protocols and spin-based quantum technologies, where preserving nonlocal correlations is essential for reliable quantum operations.
Quantum correlations are fragile under noise, motivating quantitative measures that track not only their presence but also their degradation during physical evolution. We develop a robustness framework for the hierarchy of Bell nonlocality, EPR steering, and entanglement, establishing an ordering of the corresponding robustness measures and relating robustness to noise-induced transition times. We further formulate the instantaneous robustness decay along Lindblad dynamics as a directional derivative determined by both the evolution and the robustness functional. Applications to isotropic depolarizing noise and amplitude damping illustrate, respectively, the resulting resource transition times and the directional dependence of steering robustness. The framework provides an approach to characterizing the degradation and lifetime of bipartite quantum correlations under noisy dynamics.
We investigate the quantum dynamics of coherence in the hyperfine structure of hydrogen atoms subjected to dephasing noise, modeled using the Lindblad master equation. The effective Hamiltonian describes the spin–spin interaction between the electron and proton, with dephasing introduced via Lindblad operators. Analytical solutions for the time-dependent density matrix are derived for various initial states, including separable, partially entangled, and maximally entangled configurations. Quantum coherence is quantified through the l1-norm measures, while purity is evaluated to assess mixedness. Results demonstrate that coherence exhibits oscillatory decay modulated by the dephasing rate, with antiparallel spin states showing greater resilience against noise compared to parallel configurations. These findings highlight the interplay between coherent hyperfine dynamics and environmental dephasing, offering insights into preserving quantum resources in atomic systems for applications in quantum information science.