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We present a scheme for non-deterministically approximating photon numberresolving detectors using non-discriminating detectors. The model is simple inconstruction and employs very few physical resources. Despite itsnon-determinism, the proposal may nonetheless be suitable for use in somequantum optics experiments in which non-determinism can be tolerated. Weanalyze the detection scheme in the context of an optical implementation of thecontrolled-NOT gate, an inherently non-deterministic device. This allows thegate's success probability to be traded away for improved gate fidelity,assuming high efficiency detectors. The scheme is compared to two otherproposals, both deterministic, for approximating discriminating detectors usingnon-discriminating detectors: the cascade and time division multiplexingschemes.Comment: 5 pages, 7 figures (published version

Non-deterministic approximation of photon number discriminating detectors using non-discriminating detectors