Efficient entanglement purification for Greenberger-Horne-Zeilinger states via the distributed parity-check detector

A scheme is proposed to implement multipartite entanglement purification of quantum systems in a Greenberger-Horne-Zeilinger (GHZ) state by using the distributed parity-check detector and quantum non-demolition (QND) photon-number-resolving measurement based on the weak cross-Kerr nonlinearities. The prominent feature of the scheme does not need either ancillary entangled photon pairs or the iterative purification procedure. Hence this represents a huge saving in the physical resources to implement entanglement purification. For the purification protocol to improve the fidelity of the output state, it is not essential that the fidelity of the resource states shared is more than 1/4. In addition, the total success probability and fidelity of the present purification scheme can approach unit in principle. The present scheme uses only basic tools in quantum optical laboratories and can be implemented in the regime of the weak cross-Kerr nonlinearity. Therefore, this makes us more confident in the feasibility of the proposed scheme.