The Operational Model of Quantum Measurement of Kuryshkin-Wodkiewicz

K. Wodkiewicz describes Holevo-Helstrom method, and proposes his own operational model of quantum measurements as an example of using this method. It involves the quantum probability distribution function P q,p = Wψ * Wφ q,p. Here Wφ is the Wigner distribution function of the quantum state of a quantum system before measurement, Wψ is the quantum Wigner distribution function of the quantum filter before the measurement procedure. It is known that the convolution of two quantum Wigner distribution functions is positive-definite probability distribution function in phase space of a quantum system.
Quantum Wigner distribution function is uniquely related to Weyl quantization rule, which says that a classical observable A q,p corresponds to a (pseudo) differential operator OW A, whose symbol is the function A q,p. The paper states that Kuryshkin quantization rule is associated with the quantum distribution Kuryshkin-Wodkiewicz function. This quantization rule corresponds to a classical observable A q,p the operator of the observable Oψ A with the symbol AG q,p = A * Φ q,p. Here Φ q,p = 2πℏ −3 2 e−ipq ℏ ψ q ˜ ψ p, where ˜ψ p is the Fourier transform of the state function ψ q of the quantum filter.

operational model of quantum measurement, quantization rule, quantum distribution function, average values of observables, measured values of observables