Entangled state quantum detection is a new technology that combines quantum mechanics with information science, and is used in the field of target detection. It has the potential to break through traditional detection technologies in terms of sensitivity and anti-interference ability. In the field of radar detection, constant false alarm rate is a technology with important significance and application value. However, there is no research on the method of the constant false alarm rate in the entangled state quantum detection system. Aiming at this problem, in this paper a method of constant false alarm rate for the entangled state quantum detection system is proposed. In the proposed method the system's real-time estimation of noise is adopted, and the detection threshold is adjusted adaptively, so that the entangled state quantum detection system always maintains a constant false alarm rate. The simulation results show that the proposed method of constant false alarm rate is correct and effective, and can realize the function of the constant false alarm rate of the entangled state quantum detection system. The proposed method effectively improves the flexibility and adaptability of the quantum detection system, and provides a solid theoretical foundation for the practical application of entangled state quantum detection technology.