  In this paper, photonic entanglement and interference are described and
analyzed with the language of quantum information process. Correspondingly, a
photon state involving several degrees of freedom is represented in a new
expression based on the permutation symmetry of bosons. In this expression,
each degree of freedom of a single photon is regarded as a qubit and operations
on photons as qubit gates. The two-photon Hong-Ou-Mandel interference is well
interpreted with it. Moreover, the analysis reveals the entanglement between
different degrees of freedom in a four-photon state from parametric down
conversion, even if there is no entanglement between them in the two-photon
state. The entanglement will decrease the state purity and photon interference
visibility in the experiments on a four-photon polarization state.
