Quantum correlation for two-qubit systems interacting with macroscopic objects

We consider two particles of spin-[InlineEquation not available: see fulltext.] interacting with two one-dimensional N-spin arrays, respectively, which is an exactly solvable model. In this model, the one-dimensional N-spin arrays can be regarded as a macroscopic medium if we consider the number N of spins being large enough. In this paper, we investigate the dynamics of entanglement and quantum discord of the spins of two particles in the case of two particles passing through the macroscopic mediums synchronously and out-sync. In both case, we can obtain that the entanglement decreases monotonically with time and may suffer a sudden death in the evolution. Different from the entanglement dynamics, quantum discord first remains unchanged during a period of time and decreases later, which can be described as the sudden transition between classical and quantum decoherence. We also observe that the entanglement and quantum discord decay to zero in the case of enough large N, which can be understood that the interaction with the macroscopic medium can destroy the quantum correlation of a two-qubit system.