Features of three-photon polarization states: Entanglement and polarization

In a general form, three-photon polarization states are superpositions of contributions from four three-photon polarization modes with four arbitrary complex coefficients. Entanglement of such states is defined as entanglement between their one-photon and two-photon parts. The degree of entanglement is found explicitly in terms of such entanglement quantifiers as the generalized concurrence, entropy of reduced states and the Schmidt parameter. Polarization Stokes vectors, as well as the Schmidt decompositions of three-photon states are found and discussed. Similarity and differences with respect to biphoton polarization states are discussed too.