Entanglement of distant atoms by projective measurement: The role of   detection efficiency
  We assess proposals for entangling two distant atoms by measurement of emitted photons, analyzing how their performance depends on the photon detection efficiency. We consider schemes based on measurement of one or two photons and compare them in terms of the probability to obtain the detection event and of the conditional fidelity with which the desired entangled state is created. Based on an unravelling of the master equation, we quantify the parameter regimes in which one or the other scheme is more efficient, including the possible combination of the one-photon scheme with state purification. In general, protocols based on one-photon detection are more efficient in set-ups characterized by low photon detection efficiency, while at larger values two-photon protocols are preferable. We give numerical examples based on current experiments. 
Stefano Zippilli, Georgina A. Olivares-Renteria, Giovanna Morigi,   Carsten Schuck, Felix Rohde, Juergen Eschner