We present a way for entanglement purification based on two parametric down-conversion (PDC) sources with cross-Kerr nonlinearities. It is comprised of two processes. The first one is a primary entanglement purification protocol for PDC sources with nondestructive quantum nondemolition (QND) detectors by transferring the spatial entanglement of photon pairs to their polarization. In this time, the QND detectors act as the role of controlled-NOT (CNOT) gates. Also they can distinguish the photon number of the spatial modes, which provides a good way for the next process to purify the entanglement of the photon pairs kept more. In the second process for entanglement purification, new QND detectors are designed to act as the role of CNOT gates. This protocol has the advantage of high yield and it requires neither CNOT gates based on linear optical elements nor sophisticated single-photon detectors, which makes it more convenient in practical applications.
We present an efficient multipartite entanglement purification protocol (MEPP) for
N-photon systems in a Greenberger-Horne-Zeilinger state with parity-check detectors. It contains two parts. One is the conventional MEPP with which the parties can obtain a high-fidelity
N-photon ensemble directly, similar to the MEPP with controlled-not gates. The other is our recycling MEPP in which the entanglement link is used to produce some
N-photon entangled systems from entangled ${N}^{\ensuremath{'}}$-photon subsystems ($2\ensuremath{\leqslant}{N}^{\ensuremath{'}}<N$) coming from the instances which are just discarded in all existing conventional MEPPs. The entangled ${N}^{\ensuremath{'}}$-photon subsystems are obtained efficiently by measuring the photons with potential bit-flip errors. With these two parts, the present MEPP has a higher efficiency than all other conventional MEPPs.