  The single-photon quantum filtering problems have been investigated recently
with applications in quantum computing. In practice, the detector responds with
a quantum efficiency of less than unity since there exists some mode mismatch
between the detector and the system, and the single-photon signal may be
corrupted by quantum white noise. Consequently, quantum filters based on
multiple measurements are designed in this paper to improve the estimation
performance. More specifically, the filtering equations for a two-level quantum
system driven by a single-photon input state and under multiple measurements
are presented in this paper. Four scenarios, 1) two diffusive measurements with
Q-P quadrature form, 2) two diffusive measurements with Q-Q quadrature form, 3)
diffusive plus Poissonian measurements, and 4) two Poissonian measurements, are
considered. It is natural to compare the filtering results, i.e., measuring
single channel or both channels, which one is better? By the simulation where
we use a single photon to excite an atom, it seems that multiple measurements
enable us to excite the atom with higher probability than only measuring single
channel. In addition, measurement back-action phenomenon is revealed by the
simulation results.
