Spectrally uncorrelated biphoton state generated from the spontaneous nonlinear optical process is an important resource for quantum information. Currently such spectrally uncorrelated biphoton state can only be prepared from limited kinds of nonlinear media, thus limiting their wavelengths. In order to explore wider wavelength range, here we theoretically study the generation of spectrally uncorrelated biphoton state from 14 isomorphs of potassium dihydrogen phosphate (KDP) crystal. We find that 11 crystals from the `KDP family still maintain similar nonlinear optical properties of KDP, such as KDP, DKDP, ADP, DADP, ADA, DADA, RDA, DRDA, RDP, DRDP and KDA, which satisfy 3 kinds of the group-velocity matching conditions for spectrally uncorrelated biphoton state generation from near-infrared to telecom wavelengths. Based on the uncorrelated biphoton state, we investigate the generation of heralded pure-state single photon by detecting one member of the biphoton state to herald the output of the other. The purity of the heralded single photon is as high as 0.98 without using a narrow-band filter; the Hong-Ou-Mandel interference from independent sources can also achieve a visibility of 98%. This study may provide more and better single-photon sources for quantum information processing at near-infrared and telecom wavelengths.
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