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Propagation-based phase contrast computed tomography (PB-PCCT) is an effective technique for three-dimensional visualization of weakly attenuating samples. However, the high radiation dose caused by the long sampling time has hindered the wider adoption of PB-PCCT. By incorporating the physical imaging model of PB-PCCT with a deep neural network, this Letter develops a physics-informed deep learning reconstruction framework for sparse-view PB-PCCT. Simulation and real experiments are performed to validate the effectiveness and capability of the proposed framework. Results show that the proposed framework obtains phase-retrieved and streaking artifacts removed PB-PCCT images from only one sparse-view measured intensity without any pretrained network and labeled data.