Detection devices in entanglement-based optical state preparation

We study the use of detection devices in entanglement-based state preparation. In particular we consider optical detection devices such as single-photon sensitivity detectors, single-photon resolution detectors, and detector cascades ~with an emphasis on the performance of realistic detectors!. We develop an extensive theory for the use of these devices. In entanglement-based state preparation we perform measurements on subsystems, and we therefore need precise bounds on the distinguishability of these measurements ~this is fundamentally different from, e.g., tomography, where an ensemble of identical states is used to determine probability distributions, etc.!. To this end, we introduce the confidence of preparation, which may also be used to quantify the performance of detection devices in entanglement-based preparation. We give a general expression for detector cascades of arbitrary size for the detection up to two photons. We show that, contrary to the general belief, cascading does not give a practical advantage over detectors with single-photon resolution in entanglement-based state preparation.