  Multiphoton entanglement, as a quantum resource, plays an essential role in
linear optical quantum information processing. Krenn et al. (Phys. Rev. Lett.
118, 080401 2017) proposed an innovative scheme that generating entanglement by
path identity, in which two-photon interference (called Hong-Ou-Mandel effect)
is not necessary in experiment. However, the experiments in this scheme have
strict requirements in stability and scalability, which is difficult to be
realized in bulk optics. To solve this problem, in this paper we first propose
an on-chip scheme to generate multi-photon polarization entangled states,
including Greenberger-Horne-Zeilinger (GHZ) states and W states. Moreover, we
also present a class of generalized graphs for W states (odd-number-photon) by
path identity in theory. The on-chip scheme can be implemented in existing
integrated optical technology which is meaningful for multi-party entanglement
distribution in quantum communication networks.
