Use of discrete Wigner functions in the study of decoherence of a system of superconducting flux-qubits

The persistence of coherence of a system of superconducting flux-qubits, in the presence of an ensemble of electrons, is analysed. The time evolution of the system is solved exactly. We study the time evolution of the Wigner function of the reduced density matrix of the qubits, in order to determine the rate of decoherence induced by the coupling with the electrons. We found that the rate of induced decoherence may be reduced, depending on the interactions with the electrons. Also, we discuss the squeezing properties of the system.