Entanglement dynamics of two-qubit pure state

We show that the entanglement dynamics for the pure state of a closed two-qubit system is part of a 10-dimensional complex linear differential equation defined on a supersphere, and the coefficients therein are completely determined by the system Hamiltonian. We apply the result to two physical examples of Josephson junction qubits and exchange Hamiltonians, deriving analytic solutions for the time evolution of entanglement. The Hamiltonian coefficients determine whether the entanglement is periodic. These results allow of investigating how to generate and manipulate entanglements efficiently, which are required by both quantum computation and quantum communication.