We　propose　an　efficient　protocol　for　W　polarization　entangled　state　distribution　over　an　arbitrary　collective-noise　channel　with　the　help　of　the　cross-Kerr　nonlinearity.　The　entangled　state　in　the　frequency　degree　of　freedom,　which　suffers　little　from　the　noise　in　an　optical　fiber,　is　used　in　the　present　protocol.　The　frequency　entanglement　can　be　transferred　into　polarization　entanglement　with　the　success　probability　of　100%.　So,　the　three　parities　can　share　the　maximally　W　polarization　state　with　local　operations　and　polarization　independent　wavelength　division　multiplexers　which　can　erase　distinguishability　for　frequency.　Crown　Copyright　(C)　2011　Published　by　Elsevier　B.V.　All　rights　reserved.