  Pure dephasing processes limit the fidelities achievable in
driven-dissipative schemes for stabilization of entangled states of qubits. We
propose a scheme which, combined with already existing entangling methods,
purifies the desired entangled state by driving out of equilibrium auxiliary
dissipative cavity modes coupled to the qubits. We lay out the specifics of our
scheme and compute its efficiency in the particular context of two
superconducting qubits in a cavity-QED architecture, where the strongly coupled
auxiliary modes provided by collective cavity excitations can drive and sustain
the qubits in maximally entangled Bell states with fidelities reaching 90% for
experimentally accessible parameters.
