We develop the quantizer–dequantizer formalism for the probability and mean-value representations of qubits and qutrits. In these representations, the elements of symbols of operators are measurable physical quantities. We derive the star-product kernels, which lead to explicit expressions of the associative product of the symbols of the density operators and quantum observables for qubits. The extension of the quantizer–dequantizer formalism associated with the probability and mean-value descriptions of qudit states is discussed.

中文翻译：

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星级产品形式主义的Qudits概率和均值表示

我们开发了量化器-均衡器形式主义，以表示量子位和Qutrit的概率和均值。在这些表示中，运算符符号的元素是可测量的物理量。我们推导出星积核，该核积导致密度算符符号和量子可观量子位的符号的联想乘积的明确表示。讨论了量化器-均衡器形式主义与Qudit状态的概率和均值描述相关的扩展。