  We analyze a controllable generation of maximally entangled mixed states of a
circuit containing two-coupled superconducting charge qubits. Each qubit is
based on a Cooper pair box connected to a reservoir electrode through a
Josephson junction. Illustrative variational calculations were performed to
demonstrate the effect on the two-qubits entanglement. At sufficiently
deviation between the Josephson energies of the qubits and/or strong coupling
regime, maximally entangled mixed states at certain instances of time is
synthesized. We show that entanglement has an interesting subsequent time
evolution, including the sudden death effect. This enables us to completely
characterize the phenomenon of entanglement sharing in the coupling of two
superconducting charge qubits, a system of both theoretical and experimental
interest.
