Abstract This paper investigates quantum correlations between two identical spin-1/2 particles linked by long-range dipolar interactions. A time-dependent symmetric cross-spin interaction and an external homogeneous magnetic field that varies with time are also applied to the system. Quantum correlations, such as entanglement, steering, and steered quantum coherence, are quantified using concurrence, three-steering functions, and the l 1 norm measure of coherence, respectively. These quantum correlations are examined based on the direction of interaction for dipole–dipole interactions along either the x-axis or z-axis and are symmetric concerning Zeeman energy along these axes. The maximal bounds of all three quantifiers are obtained by increasing the frequency of the time-dependent and symmetric coupling parameters. These maximal bounds significantly strengthen when considering symmetric and Zeeman interactions along the x-axis; however, the pinnacle of entanglement is reached in perpendicular configurations.
Abstract This paper investigates quantum correlations between two identical spin-1/2 particles linked by long-range dipolar interactions. A time-dependent symmetric cross-spin interaction and an external homogeneous magnetic field that varies with time are also applied to the system. Quantum correlations, such as entanglement, steering, and steered quantum coherence, are quantified using concurrence, three-steering functions, and the l 1 norm measure of coherence, respectively. These quantum correlations are examined based on the direction of interaction for dipole–dipole interactions along either the x-axis or z-axis and are symmetric concerning Zeeman energy along these axes. The maximal bounds of all three quantifiers are obtained by increasing the frequency of the time-dependent and symmetric coupling parameters. These maximal bounds significantly strengthen when considering symmetric and Zeeman interactions along the x-axis; however, the pinnacle of entanglement is reached in perpendicular configurations.
Quantum correlations between a pair of spin-1/2 represented by an XYZ-Heisenberg chain are investigated under symmetric, anti-symmetric and long-range dipolar interactions. Entanglement, steering, and nonlocality are quantified through concurrence, 3-steering functions, and normalized Bell functions, respectively. By modulating interaction directions, effects on quantum correlations are elucidated for two scenarios: dipolar coupling along x or z, with symmetric and anti-symmetric terms oriented perpendicular or parallel. The results indicate that quantum correlations are enhanced when dipolar coupling aligns with the z-direction versus the x-direction. Moreover, increasing long-range dipolar interaction strength degrades the quantum correlations for weaker Heisenberg chain coupling. Positioning symmetric and anti-symmetric couplings along the z-direction affect quantum correlation dissipation at a critical point. Furthermore, with symmetric and anti-symmetric terms oriented along x, quantum correlations diminish for x-direction dipolar coupling.
Abstract The concepts of concurrence, 3-steerability, and Clauser–Horne–Shimony–Holt (CHSH) inequality are employed to investigate the environmental impacts on the quantum correlations of the two-spin-1/2 Heisenberg XYZ chain model. In particular, the effects of a homogeneous magnetic field, symmetric cross interaction, and dipole–dipole interaction on the entanglement, degree of steerability, and non-locality are discussed. Results show that the entanglement and steering phenomena are bounded by the non-locality for both positive and negative values of dipole–dipole coupling. It has also been observed that higher symmetric cross-interaction strengthens the quantum correlations, whereas the homogeneous magnetic field weakens the quantumness of the system. The findings indicate that a magnetic field normal to the magnetic dipole yields better quantum correlations than when they are parallel.
In this paper a system consisting of two electron spins has been prepared initially in a singlet state using the chemical compass model is considered. It is assumed that each electron spin interacts symmetrically and/or asymmetrically with its respective private nuclear environment in the presence of an external magnetic field. We discussed the effect of the interaction parameters and the external magnetic field on some quantifiers of quantum correlations as entanglement, coherence, Bell inequality, as well as the steerability inequality. It is shown that within a certain range of external magnetic fields, the quantum coherence and entanglement behave similarly. The Bell and the steerable inequalities predicted a similar behavior for symmetric and asymmetric interactions. Moreover, as one increases the external magnetic field, the lower bounds of both inequalities have improved. The usefulness of using the spin state as quantum channel to teleport a two-qubit system has examined where the Bell inequality could be above its classical bounds by controlling the interaction parameters. It is shown that by tuning the coupling parameters the fidelity of the teleported state exceeds the classical bounds, as well as the long-lived stationary fidelity could be achieved during the interaction time.
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.
We address the dynamics of quantum coherence, quantum correlations, quantum steering and Bell nonlocality in a model of two interacting qubits, initially prepared in a thermal state. The two qubit are coupled via a dipolar interaction and exposed to Dzyaloshinskii–Moriya (DM) interaction and classical fluctuating fields influenced by Ornstein–Uhlenbeck (OU)-Static (ST) mixed noise in common environments. We analyse the dynamics effects on quantum resources, as Bell nonlocality, quantum steering, quantum entanglement, quantum discord and quantum coherence. We find that the dynamics of quantum correlations are not only strongly affected by the type of system-environment coupling but also by the kind of the considered noise. The entanglement diminution is over time, accompanied by damped oscillations, indicative of coherent dynamics. The DM interaction induces a decrease in quantum coherence and correlations with increasing values, leading to complete maximizing at critical thresholds. The effects of thermal effects destroy the quantum correlation. The variations in state noise disorder parameters reveal enhanced preservation and reduced oscillations as the noise disorder parameter decreases, emphasizing its crucial role in shaping quantum correlations.
An analytical solution is obtained for the problem of two interacting, identical but separated spin 1/2 particles in a time-dependent external magnetic field, in a general case. The solution involves isolating the pseudo-qutrit subsystem from a two-qubit system. It is shown that the quantum dynamics of a pseudo-qutrit system with a magnetic dipole-dipole interaction can be described clearly and accurately in an adiabatic representation, using a time-dependent basis set. The transition probabilities between the energy levels for an adiabatically varying magnetic field, which follows the Landau-Majorana-Stuckelberg-Zener (LMSZ) model within a short time interval, are illustrated in the appropriate graphs. It is shown that for close energy levels and entangled states, the transition probabilities are not small and strongly depend on the time. These results provide insight into the degree of entanglement of two spins (qubits) over time. Furthermore, the results are applicable to more complex systems with a time-dependent Hamiltonian.