Star Product Formalism for Probability and Mean Value Representations of Qudits

The quantizer-dequantizer formalism is developed for mean value and probability representation of qubits and qutrits. We derive the star-product kernels providing the possibility to derive explicit expressions of the associative product of the symbols of the density operators and quantum observables for qubits. We discuss an extension of the quantizer-dequantizer formalism associated with the probability and observable mean-value descriptions of quantum states for qudits.