  We investigate the effect of imperfections in realistic detectors upon the
problem of quantum state and parameter estimation by continuous monitoring of
an open quantum system. Specifically, we have reexamined the system of a
two-level atom with an unknown Rabi frequency introduced by Gambetta and
Wiseman [Phys. Rev. A 64, 042105 (2001)]. We consider only direct
photodetection and use the realistic quantum trajectory theory reported by
Warszawski, Wiseman, and Mabuchi [Phys. Rev. A 65, 023802 (2002)]. The most
significant effect comes from a finite bandwidth, corresponding to an
uncertainty in the response time of the photodiode. Unless the bandwidth is
significantly greater than the Rabi frequency, the observer's ability to obtain
information about the unknown Rabi frequency, and about the state of the atom,
is severely compromised. This result has implications for quantum control in
the presence of unknown parameters for realistic detectors, and even for ideal
detectors, as it implies that most of the information in the measurement record
is contained in the precise timing of the detections.

Quantum Physics