Propensities in discrete phase spaces:Qfunction of a state in a finite-dimensional Hilbert space

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Abstract
We present a Q function of a state of a quantum-mechanical system in a finite-dimensional Hilbert space. This discrete Q function is defined with the help of the Wódkiewicz concept of propensities, i.e., we define the Q function as a discrete convolution of two Wigner functions based on Wootter’s formalism, one of the state itself and one of the filter state. The discrete Q function takes nonnegative values in all ‘‘points’’ of the discrete phase space and is normalized and it is possible to reconstruct from it the density operator of the state under consideration. We analyze Q-function graphs for several states of interest.