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The generation of Bell states of distant objects is of importance forconstructing quantum networks. Previous studies have revealed that transient orintermittent Bell states can be generated between remote qubits by exploitingtime-continuous measurement on the environments of the systems, e.g., photoncounting or homodyne detection. In this paper, we consider a new scheme forachieving long-time sustainable Bell states of two distant qubits mediated by aone-dimension waveguide via continuous photon counting and homodyne detection.In both of cases, different Bell states can be present for different initialstates in the long-time regime. Specially, in the former case, we find that acyclic jump among Bell states can be formed once the first photon isregistered, and more interestingly in the latter case, any steady Bell statecan be achieved independent of detection efficiency.

Long-time Bell states of waveguide-mediated qubits via continuous measurement