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We propose two optimal entanglement concentration protocols (ECPs) forarbitrary single-photon multi-mode W state and multi-photon polarization Wstate, respectively. In both ECPs, we only require one pair of partiallyentangled W state, and do not consume any auxiliary photon. Both ECPs are basedon the linear optics which can be easily realized. On the other hand, theconcentrated maximally entangled states can be remained, which are quitedifferent from the previous ECPs. Moreover, for the concentration of thearbitrary single-photon N-mode W state or N-mode polarization W state, thetotal success probability is equal to Nth the modulus square of the Schmidtcoefficient of the smallest magnitude. It makes both ECPs optimal than all theprevious ECPs. Our ECPs may be useful in current quantum communication fields.

Optimal concentrating arbitrary partially entangled W states with linear optics