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Tensor compressed sensing (TCS) from binary measurements aims to recover a tensor with low-rankness from the binary quantization of its degraded linear measurements, which inherits the advantages of low equipment cost and high sampling efficiency of coarse quantization. Recently, numerous studies have demonstrated that incorporating the properties of low-rankness and local smoothness, which are commonly observed in practical tensor data, can significantly enhance conventional tensor recovery tasks. This motivates us to utilize the low-rank and smooth properties in solving TCS problems from binary measurements. Equipped with the recently proposed tensor correlated total variation (TCTV) that simultaneously regularizes low-rankness and smoothness, we present a regularized model for this problem in this paper. We rigorously prove the recovery guarantee for the proposed model and provide an explicit selection rule for the regularization parameter. Moreover, the theoretical results demonstrate the robustness of the proposed method against both bit flips and pre-quantization noises. An algorithm based on alternating direction multiplier method (ADMM) is presented for solving the proposed model, with its global convergence been proven. Finally, a series of experiments demonstrate the superior performance of our method compared to many other competing approaches. • A method for tensor recovery from binary measurements which codes both low-rankness and smoothness was proposed. • We prove a recovery guarantee for the method and provide an explicit selection rule for the regularization parameter. • The method is robust to bit flips and pre-quantization noises, two common noises in one-bit quantization. • The proposed model can be solved using the alternating direction multiplier method with global convergence. [ABSTRACT FROM AUTHOR]