Dynamics of Superconducting Flux-Qubit Measurements by Dc-Squid

In experiments of superconducting flux-qubit, a dc-SQUID has been used to read-out the qubit state. The value really obtained by the measurement is the switching current (I_SW) of the SQUID. In order to clarify the relation between the I_SW and the qubit state, we calculated the time evolution of a composite system consisting of a dc-SQUID and flux-qubit. The entanglement formation and the transition to mixed-states, which are caused by the interaction between the SQUID and the qubit, are discussed.