High-order dispersion of long-range surface-plasmon-polariton waveguides (LR-SPP-WGs) have been investigated using a two-photon interferometer. Since linear and even-ordered dispersions in two-photon interferometry are cancelled out by a nonlocal quantum correlation, odd-ordered dispersions of millimeter-long LR-SPP-WGs are revealed. Even under the highly dispersive condition, the indistinguishability between two photons emerged from LR-SPP-WGs was well preserved. In addition, we demonstrated a strong polarization-selection by the LR-SPP-WGs that leads to the polarization-stable and high-fidelity quantum interference. (C) 2017 Optical Society of America