We present an 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 one uses the quantum nondemolition (QND) to construct the complete parity check gate. Both of which can achieve the concentration task. These protocols have several advantages. First, it 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, in the second protocol, it can be repeated to perform the concentration step and get a higher success probability. All these advantages make it be useful in current quantum communication and computation applications.
We describe an efficient way for measuring the concurrence of the hyperentanglement. In this protocol, the hyperentangled state is encoded in both polarization and momentum degrees of freedom. We show that the concurrences of both polarization and momentum entanglement can be conversed into the total success probability of picking up the odd-parity state and can be measured directly. This protocol requires the weak cross-Kerr nonlinearity to construct the quantum nondemolition measurement and does not resort to the sophisticated controlled-not gate operation. It is feasible in current experimental technology.
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