Hollow-core fiber (HCF) promises to unify air-borne light propagation and non-line-of-sight transmission, thus holding great potential for versatile photonics-based quantum information applications. The early version of HCF based on photonic-bandgap guidance has not proven itself a reliable quantum channel because of the poor modal purity in both spatial and polarization domains, as well as significant difficulty in fabrication when the wavelength shifts to the visible region. In this work, based on the polarization degree of freedom, we demonstrate high-fidelity ( ∼ 0.98 ) single-photon transmission and distribution of entangled photons over a 36.4 m hollow-core conjoined-tube fiber (CTF) by using commercial silicon single-photon avalanche photodiodes. Our CTF realizes the combined merits of low loss, high spatial modal purity, low polarization degradation, and low chromatic dispersion. We also demonstrate single-photon low-latency ( ∼ 99.96 % speed of light in vacuum) transmission, paving the way for extensive uses of HCF links in versatile photonics-based quantum information processing.