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The dynamics of entanglement and fidelity for a subsystem of two separatespin-1/2 qubits prepared in Bell states is investigated. One of the subsystemqubit labelled $A$ is under the influence of a Heisenberg XY spin-bath, whileanother one labelled $B$ is uncoupled with that. We discuss two cases: (i) thenumber of bath spins $N\to\infty$; (ii) $N$ is finite: N=40. In both cases, thebath is initially prepared in a thermal equilibrium state. It is shown that thetime dependence of the concurrence and the fidelity of the two subsystem qubitscan be controlled by tuning the parameters of the spin-bath, such as theanisotropic parameter, the temperature and the coupling strength with qubit$A$. It is interesting to find the dynamics of the concurrence is independentof four different initial Bell states and that of the fidelity is divided intotwo groups.

Controllable dynamics of two separate qubits in Bell states