We study the dynamics of quantum nonlocality in a graphene-inspired two-carbon-atom Fermi-Hubbard system. Three measures of quantum correlation are examined. These are the entanglement of formation, the Einstein-Podolsky-Rosen steering, and the violation of the CHSH inequality. The system is modelled by the extended Hubbard Hamiltonian with on-site and nearest-neighbour Coulomb interactions, and intrinsic decoherence is described by Milburn's model. The half-filled sector, the two-qubit encoding and the initial state are specified. The two Coulomb energies act through their difference alone. This difference fixes a fast timescale set by the charge gap and a slow timescale set by the superexchange splitting. The level of correlation that the system reaches is fixed by the preparation. Intrinsic decoherence removes the fast component before the slow one, so the lifetime of the nonlocal correlations grows as the difference of the Coulomb energies grows. The entanglement of formation survives after the nonlocal measures have vanished.
We study the dynamics of quantum nonlocality in a graphene-inspired two-carbon-atom Fermi-Hubbard system. Three measures of quantum correlation are examined. These are the entanglement of formation, the Einstein-Podolsky-Rosen steering, and the violation of the CHSH inequality. The system is modelled by the extended Hubbard Hamiltonian with on-site and nearest-neighbour Coulomb interactions, and intrinsic decoherence is described by Milburn's model. The half-filled sector, the two-qubit encoding and the initial state are specified. The two Coulomb energies act through their difference alone. This difference fixes a fast timescale set by the charge gap and a slow timescale set by the superexchange splitting. The level of correlation that the system reaches is fixed by the preparation. Intrinsic decoherence removes the fast component before the slow one, so the lifetime of the nonlocal correlations grows as the difference of the Coulomb energies grows. The entanglement of formation survives after the nonlocal measures have vanished.
Abstract In this paper, we study the dynamics of Bell nonlocality and quantum steering of Fermi-Hubbard model on graphene honeycomb lattice. In the model, Bell nonlocality and Einstein-Podolski-Rosen steering have been exactly solved with and without the local flltering operation (LFO). The influence of flnite temperature, on-site Coulomb repulsion, and nearest-neighbor repulsion on Bell nonlocality and quantum steerability is investigated. The equilibrium state established through the competition between nearest-neighbor and on-site Coulomb repulsions efiectively balances nonlocal quantum correlations. The interplay of these competing interactions drives the system toward a separable regime, wherein both Bell nonlocality and quantum steering violations are completely suppressed. Furthermore, the flltering process not only enhances the degree of quantum steering and Bell nonlocality but also contracts their operational range. These results will provide more theoretical guidance and greater practical signiflcance for the manipulation of Bell nonlocality and quantum steering within graphene systems.
Quantum correlation is an important resource in quantum information, quantum computation, and quantum metrology. Quantum entanglement, Einstein-Podolsky-Rosen (EPR) quantum steering and Bell nonlocality are the major quantum correlations. For quantum entanglement and Bell nonlocality, two subsystems play the same significant roles. EPR quantum steering is stronger than entanglement and weaker than Bell nonlocality. It represents the ability of one subsystem to nonlocally affect another subsystem's states through local measurements. In this paper, the dynamic quantum correlation between the modes in the two-site Bose-Hubbard model is investigated. According to Hillery-Zubairy entanglement criterion and based on maximum mean quantum Fisher information, the influences of initial states on the quantum entanglement evolutions are explored. If the coupling between the modes is much greater than that of the particles at the same site, and the initial states are symmetric or anti-symmetric SU(2) coherent states, the quantum correlations show simple periodic evolutions. The oscillation amplitudes of the evolutions increase with the interaction between the particles at the same site. The oscillation period decreases with the coupling strength between the modes. The dependence of the period on the interaction of the particles at the same site is related to the initial states. In other words, the time evolutions of quantum correlation are closely related to the symmetry of the initial states. In the case of symmetric (anti-symmetric) SU(2) coherent state and repulsive (attractive) interaction of the particles at the same site, the system presents two-way quantum steering. When the subsystem exchange symmetry of the initial states is broken, the collapse and revival of quantum correlation appear, moreover one-way quantum steering emerges in the infancy. One-way quantum steering is asymmetric for two subsystems. So exchange asymmetry of the initial state is necessary condition of one-way quantum steering when the Hamiltonian of the system is symmetric for two subsystems.
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.
By using the Born Markovian master equation, we study the relationship among the Einstein-Podolsky-Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.
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.
Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set of all Bell local states and the set of all EPR unsteerable states. We also derive a EPR-steering criteria, with which the EPR steerability of the maximally entangled states are checked.