  We present two two-step practical entanglement concentration protocols (ECPs)
for concentrating an arbitrary three-particle less-entangled W state into a
maximally entangled W state assisted with single photons. The first protocol
uses the linear optics and the second protocol adopts the cross-Kerr
nonlinearity to perform the protocol. In the first protocol, based on the
post-selection principle, three parties say Alice, Bob and Charlie in different
distant locations can obtain the maximally entangled W state from the arbitrary
less-entangled W state with a certain success probability. In the second
protocol, it dose not require the parties to posses the sophisticated
single-photon detectors and the concentrated photon pair can be retained after
performing this protocol successfully. Moreover, the second protocol can be
repeated to get a higher success probability. Both protocols may be useful in
practical quantum information applications.
