We　propose　an　efficient　nonlocal　entanglement　distribution　protocol　(EDP)　to　purify　the　two-photon　polarization-entangled　state,　resorting　to　the　projection　measurement　on　the　additional　photons.　With　the　help　of　the　cross-Kerr　nonlinearity,　two　remote　parties　can　share　two-photon　maximally　entangled　polarization　state　from　the　arbitrary　two-photon　states　with　a　certain　success　probability　by　iterating　the　entanglement　purification　process　6　times.　Compared　with　conventional　EDPs,　the　present　one　can　obtain　maximally　entangled　polarization　state　over　an　collective-noise　channel　with　deterministic　success　probability.　That　is,　the　EDP　is　an　optimal　one.　©　2013　Springer　Science+Business　Media　New　York.