Controllable dynamics of two separate qubits in Bell states

Abstract

The dynamics of entanglement and fidelity for a subsystem of two separate spin-$1∕2$ qubits prepared in Bell states is investigated. One of the subsystem qubit labeled $A$ is under the influence of a Heisenberg $XY$ spin bath, while another one labeled $B$ is uncoupled with that. We discuss two cases: (i) the number of bath spins is infinite, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, and (ii) $N$ is finite, $N=40$. In both cases, the bath is initially prepared in a thermal equilibrium state. It is shown that the time dependence of the concurrence and the fidelity of the two subsystem qubits can be controlled by tuning the parameters of the spin bath, such as the anisotropic parameter, the temperature, and the coupling strength with qubit $A$. It is interesting to find that the dynamics of the concurrence is independent of four different initial Bell states and that of the fidelity is divided into two groups.