We experimentally demonstrate a high-fidelity entanglement swapping and ageneration of the Greenberger-Horne-Zeilinger~(GHZ) state usingpolarization-entangled photon pairs at telecommunication wavelength produced byspontaneous parametric down conversion with continuous-wave pump light. Whilespatially separated sources asynchronously emit photon pairs, the time-resolvedphoton detection guarantees the temporal indistinguishability of photonswithout active timing synchronizations of pump lasers and/or adjustment ofoptical paths. In the experiment, photons are sufficiently narrowed byfiber-based Bragg gratings with the central wavelengths of 1541~nm and 1580~nm,and detected by superconducting nanowire single-photon detectors with lowtiming jitters. Observed fidelities are 0.84 \pm 0.04 and 0.70 \pm 0.05 for theentanglement swapping and generation of the GHZ state, respectively.
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