Thermal and phase decoherence effects on entanglement dynamics of the quantum spin systems

Entanglement dynamics of the N-qubit XY model in thermal and dephasing environments are investigated by solving the Lindblad form of the master equation. Analytical solutions for the two-qubit case and numerical solutions for the multi-qubit case are obtained. For the two-qubit case, our results revealed two main features for entanglement evolution from different initial states. First, the thermal reservoir always induces degradation of the entanglement, and the entanglement may undergo sudden death during certain intervals of the evolution time. Second, the dephasing environment induces damped oscillation of the entanglement for initially separable states and mixed states with relative large values of Δ or J; however, it always induces exponentially decay of the entanglement for the initial Bell states. For the multi-qubit case, our results show that the entanglement decreases monotonically as the time evolves for the initial W state, and behaves as damped oscillation for the initial “one-particle” state. Particularly, for system with large number of qubits, the curves of the concurrence C₁₂ with different N are almost overlapped in dephasing environment.