Following Kenfack and Życzkowski, we consider the indicator of nonclassicality of quantum states for N−level systems defined via the integral of the absolute value of the Wigner function. For these systems, remaining in the framework of Stratonovich-Weyl correspondence, one can construct a whole family of representations of the Wigner functions defined over the continuous phase-space and characterized by a set of $(N-2)$ moduli parameters. It is shown that the nonclassicality indicator, being invariant under the $SU(N)$ transformations of states, turns to be sensitive to the representation of the Wigner function. We analyse this representation dependence computing the Kenfack-Życzkowski indicators for pure and mixed states of a 3-level system using a generic and two degenerate Stratonovich-Weyl kernels respectively. Our calculations reveal three classes of states: the “absolutely classical/quantum” states, which have zero and non-vanishing indicator for all values of the moduli parameters correspondingly, and the “relatively quantum-classical” states whose classicality/quantumness is susceptible to a representation of the Wigner function. Herewith, all pure states of qutrit belong to the “absolutely quantum” states.

继 Kenfack 和 Życzkowski 之后，我们考虑了通过 Wigner 函数绝对值的积分定义的N级系统的量子态非经典性指标。对于这些系统，保留在 Stratonovich-Weyl 对应的框架中，我们可以构建在连续相空间上定义的 Wigner 函数的整个表示系列，并以一组为特征$(N-2)$模参数。结果表明，非经典性指标在$秒你(N)$状态的转换，变得对 Wigner 函数的表示敏感。我们分别使用通用和两个退化的 Stratonovich-Weyl 核来分析这种表示依赖性，计算 3 级系统的纯状态和混合状态的 Kenfack-Życzkowski 指标。我们的计算揭示了三类状态：“绝对经典/量子”状态，其对应模参数的所有值具有零和非零指示符，以及“相对量子经典”状态，其经典/量子易受Wigner 函数的表示。因此，qutrit 的所有纯态都属于“绝对量子”态。