Quantum probability measures and tomographic probability densities

Introduced recently approach based on tomographic probability distribution of quantum states is shown to be closely related with the known notion of the quantum probability measures discussed in quantum information theory and positive operator valued measures approach. Partial derivative of the distribution function of quantum probability measure associated with the homodyne quadrature (symplectic quantum measure) is shown to be equal the tomogram of the quantum state. Analogous relation of the spin tomogram to quantum probability measure associated with spin state is obtained. Star-product of symplectic quantum measures is studied. Evolution equation for symplectic quantum measures is derived.