Efficient N particle W state concentration with different parity check gates
We present a universal way to concentrate an arbitrary N particle less entangled W state into a maximally entangled W state with different parity check gates. It comprises two protocols. The first protocol is based on the linear optical elements, say the partial parity check gate and the second protocol uses the quantum nondemolition measurement to construct the complete parity check gate. Both protocols can achieve the concentration task. These protocols have several advantages. First, they can obtain a maximally entangled W state only with the help of some single photons, which greatly reduces the number of entanglement resources. Second, in the first protocol, only linear optical elements are required, which is feasible with current techniques. Third, the second protocol can be repeated to perform the concentration step and obtain a higher success probability. All these advantages make it quite useful in current quantum communication and computation applications.