Quantum Probability Measures and Tomographic Probability Densities

Abstract

Using a simple relation of the Dirac delta-function to generalized the theta-function, the relationship between the tomographic probability approach and the quantum probability measure approach with the description of quantum states is discussed. The quantum state tomogram expressed in terms of the mean value of the operator delta-function is shown to be equal to the partial derivative of the distribution function of the quantum probability measure. For spin states, the spin tomogram expressed in terms of the mean value of the operator Kronecker delta-function is related to the corresponding density operator for the quantum probability measure associated with the discrete variable. The star-product of symplectic quantum measures is studied and the evolution equation for symplectic quantum measures is derived.