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

In this paper we consider a scheme for achieving long-time sustainable Bell states of two distant qubits mediated by a one-dimensional waveguide whose outputs are subjected to time-continuous photon counting or homodyne detection. In both of the detection cases, it is shown that different Bell states can be obtained, for different initial states, in the long-time regime. In particular, we find that, in the case of photon counting, a cyclic jump among Bell states can be formed once the first photon is registered. While in the homodyne-detection case we further reveal that any steady Bell state can be achieved independent of detection efficiency, with a probability of 50% . The underlying physical reason for this is also analyzed. Our scheme is advantageous over previous studies in which only transient or intermittent Bell states can be generated. The long-time Bell states of distant qubits can be used for constructing quantum networks.