  We derived quantum trajectories for a system interacting with the environment
prepared in a continuous mode single photon state as the limit of discrete
filtering model with an environment defined as series of independent qubits
prepared initially in the entangled state being an analogue of a continuous
mode state. The environment qubits interact with the quantum system and they
are subsequently measured. The initial correlation between the bath qubits is
the source of the non-Markovianity. The conditional evolutions of the quantum
system for limit of the continuous in time observations together with the
formulas for the photon counting probabilities are given.
