  We analyze the detection of itinerant photons using a quantum non-demolition
(QND) measurement. We show that the backaction due to the continuous
measurement imposes a limit on the detector efficiency in such a scheme. We
illustrate this using a setup where signal photons have to enter a cavity in
order to be detected dispersively. In this approach, the measurement signal is
the phase shift imparted to an intense beam passing through a second cavity
mode. The restrictions on the fidelity are a consequence of the Quantum Zeno
effect, and we discuss both analytical results and quantum trajectory
simulations of the measurement process.
