We present an exact model of the detection statistics of a probabilistic source of photon pairs from which a fast, simple and precise method to measure the source's brightness and photon channel transmissions is demonstrated. We measure such properties for a source based on spontaneous parametric downconversion in a periodically poled LiNbO 3 crystal producing pairs at 810 and 1550 nm wavelengths. We further validate the model by comparing the predicted and measured values for the g (2) (0) of a heralded single photon source over a wide range of the brightness. Our model is of particular use for monitoring and tuning the brightness on demand as required for various quantum communication applications. We comment on its applicability to sources involving spectral and/or spatial filtering.

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Laser operation with a single trapped Ca+ ion in a high-finesse optical cavity is predicted at a wavelength of 866 nm. Different from a conventional laser, the formation of two thresholds can be observed. For both small and large pump strengths the field is quasi-thermal, in an intermediate region laser light with Poissonian and even sub-Poissonian statistics is produced. Atomic coherence effects play an important role. The multi-level system is treated by generalizing the pump-operator approach (Europhys. Lett., 33 (1996) 515).

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We derive lower bounds for the attainable fidelity of standard entanglement purification protocols when local operations and measurements are subjected to errors. We introduce an error parameter which measures the distance between the ideal completely positive map describing a purification step and the one in the presence of errors. We derive non-linear maps for a lower bound of the fidelity at each purification step in terms of this parameter.

We present a detailed treatment of a laser process that has been predicted for an experiment with a single trapped Ca ϩ ion. It is demonstrated how the complex multilevel system can be understood as a coherently pumped three-level scheme with time-delayed pumping out of the metastable lower laser level. This is described by a pump operator, which simplifies the numerical analysis substantially and allows for a treatment of more complicated systems. ͓S1050-2947͑98͒08809-X͔