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Terahertz (THz) systems are capable of supporting ultra-high data rates thanks to large bandwidth, and the potential to harness high-gain beamforming to combat high pathloss. In this paper, a novel quantum sensing (Ghost Imaging (GI)) based beam training is proposed for Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surface (STAR RIS) aided THz multi-user massive MIMO systems. We first conduct GI by surrounding 5G downlink signals to obtain 3D images of the environment including users and obstacles. Based on the information, we calculate the optimal position of the UAV-mounted STAR by the proposed algorithm. Thus the position-based beam training can be performed. To enhance the beam-forming gain, we further combine with channel estimation and propose a semi-passive structure of the STAR and ambiguity elimination scheme for separated channel estimation. Thus the ambiguity in cascaded channel estimation, which may affect optimal passive beamforming, is avoided. The optimal active and passive beamforming are then carried out and data transmission is initiated. The proposed BS sub-array and sub-STAR spatial multiplexing architecture, optimal active and passive beamforming, digital precoding, and optimal position of the UAV- mounted STAR are investigated jointly to maximize the average achievable sum rate of the users. Moreover, the cloud radio access networks (CRAN) structured 5G downlink signal is proposed for GI with enhanced resolution. The simulation results show that the proposed scheme achieves beam training and separated channel estimation efficiently, and increases the spectral efficiency dramatically compared to the case when the STAR operates with random phase.