  We present a scheme for non-deterministically approximating photon number
resolving detectors using non-discriminating detectors. The model is simple in
construction and employs very few physical resources. Despite its
non-determinism, the proposal may nonetheless be suitable for use in some
quantum optics experiments in which non-determinism can be tolerated. We
analyze the detection scheme in the context of an optical implementation of the
controlled-NOT gate, an inherently non-deterministic device. This allows the
gate's success probability to be traded away for improved gate fidelity,
assuming high efficiency detectors. The scheme is compared to two other
proposals, both deterministic, for approximating discriminating detectors using
non-discriminating detectors: the cascade and time division multiplexing
schemes.
