We demonstrate pulsed polarization-entangled photons generated from a periodically poled $mathrm{KTiOPO_4}$ (PPKTP) crystal in a Sagnac interferometer configuration at telecom wavelength. Since the group-velocity-matching (GVM) condition is satisfied, the intrinsic spectral purity of the photons is much higher than in the previous scheme at around 800 nm wavelength. The combination of a Sagnac interferometer and the GVM-PPKTP crystal makes our entangled source compact, stable, highly entangled, spectrally pure and ultra-bright. The photons were detected by two superconducting nanowire single photon detectors (SNSPDs) with detection efficiencies of 70% and 68% at dark counts of less than 1 kcps. We achieved fidelities of 0.981 $pm$ 0.0002 for $left| {psi ^ -} rightrangle$ and 0.980 $pm$ 0.001 for $left| {psi ^ +} rightrangle$ respectively. This GVM-PPKTP-Sagnac scheme is directly applicable to quantum communication experiments at telecom wavelength, especially in free space.
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