We present an experimental method for creating and verifying photon-numberstates created by non-degenerate, third-order nonlinear-optical photon-pairsources. By using spatially multiplexed, thresholding single-photon detectorsand inverting a conditional probability matrix, we determine the photon-numberprobabilities created through heralded spontaneous four-wave-mixing. Thedeleterious effects of noise photons on reliable heralding are investigated andshown to degrade the conditional preparation of two-photon number states morethan they degrade conditional single-photon states. We derive the equivalencebetween the presence of unwanted noise in the herald channel and loss in thesignal channel of heralded experiments. A procedure for characterizing thenoise-photon contributions, and a means of estimating the herald noise-freephoton-number distribution is demonstrated.
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