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Quantum Information Processing

Comparative analysis of nonlocal correlations and quantum-memory-assisted entropy in graphene qubits within the Hubbard model under thermal fluctuations

Zakaria Bouafia, Zakaria Dahbi, Mostafa Mansour

Published Jun 30, 2025• 6 citations
Publisher
DOI
10.1007/s11128-025-04824-4

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Exploring the role of entanglement in quantum nonequilibrium dynamics is important to understand the mechanism of thermalization in an isolated system. We study the relaxation dynamics in a one-dimensional extended Bose–Hubbard model after a global interaction quench by considering several observables: the local Boson numbers, the nonlocal entanglement entropy, and the momentum distribution functions. We calculate the thermalization fidelity for different quench parameters and different sizes of subsystems, and the results show that the degree of thermalization is affected by the distance from the integrable point and the size of the subsystem. We employ the Pearson coefficient as the measurement of the correlation between the entanglement entropy and thermalization fidelity, and a strong correlation is demonstrated for the quenched system.
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 examine the non-Markovian dynamics and the generation of quantum coherence and entanglement within a triple-layer graphene (TLG) system embedded in a planar microcavity. Using time-dependent perturbation theory, we derive an exact analytic solution for the system and demonstrate how the confined electromagnetic field mediates quantum correlations between the graphene layers. We employ three complementary measures; the relative entropy of coherence (REC) to quantify quantum coherence, the tangle to assess tripartite entanglement, and a non-Markovianity measure derived from the REC to characterize quantum memory effects. Our analysis reveals that these quantum resources exhibit remarkable sensitivity to various control parameters. Specifically, we demonstrate that the number of cutoff modes, the spatial positioning of the layers, the momentum parameter, and the interlayer rotation angles provide effective control over coherence, entanglement, and memory effects. We further show that these measures exhibit an exceptional sensitivity to the rotation angle between the layers. Ultimately, our results establish cavity-confined TLG as a highly tunable platform for exploring vacuum-mediated quantum phenomena, providing a framework for the precise manipulation of quantum correlations in graphene-based photonic and optoelectronic devices.