The theory of quantum measurements is an extremely important part of quantum. The results of the quantum measurements theory are important for experimental study of quantum-mechanical objects and verification of the theoretical structure of quantum mechanics. Developed by Holevo and Helstrom the model of quantum measurements is the most rigorous and complete from the mathematical point of view. Alternatively, a very common approach to the theory of quantum measurements is generated by the theoretical formalization of experimental measurements. The theoretical construction formed in this way is called the operational model of quantum measurements. Their equivalence established in Ozawa’s papers allowed us to describe the measured values of the quantum object using Weyl quantization rule, applied to the classical “measured quantities” obtained from the original classical quantities by convolution with Wigner function built from the quantum state functions of the probe. The result is the dissipative quantum model. © 2020, Springer Nature Switzerland AG.