On Effectiveness of Protocol Creating Maximum Entanglement of Two Charge-Phase Qubits by Cavity Field

We revisit the protocols to create maximally entangled states between two Josephson junction (JJ) charge phase qubits coupled to a microwave field in a cavity as a quantum data bus. We analyze a novel mechanism of quantum decoherence due to the adiabatic entanglement between qubits and the data bus, the off-resonance microwave field. We show that even if the variable of the data bus can be adiabatically eliminated, the entanglement between the qubits and data bus remains and can decohere the superposition of two-particle state. Fortunately we can construct a decoherence-free subspace of two-dimension to against this adiabatic decoherence. To carry out the analytic study for this decoherence problem, we develop Fröhlich transformation to re-derive the effective Hamiltonian of these systems, which is equivalent to that obtained from the adiabatic elimination approach.