We propose a method to define quasiprobability distributions for general spin-j systems of dimension $n=2j+1$, where n is a prime or power of prime. The method is based on a complete set of orthonormal commuting operators related to Mutually Unbiased Bases which enable (i) a parameterisation of the density matrix and (ii) construction of measurement operators that can be physically realised. As a result we geometrically characterise the set of states for which the quasiprobability distribution is non-negative, and can be viewed as a joint distribution of classical random variables assuming values in a finite set of outcomes. The set is an $(n^2-1)$-dimensional convex polytope with $n+1$ vertices as the only pure states, $n^{n+1}$ number of higher dimensional faces, and $n^3(n+1)/2$ edges.

我们提出了一种方法来定义一般自旋j维系统的拟拟概率分布$ñ=\mathrm{2个}Ĵ+\mathrm{1个}$，其中n是素数或素数的幂。该方法基于与互不偏基相关的一整套正交换向算子，该算子使（i）密度矩阵的参数化和（ii）可以物理实现的测量算子的构造成为可能。结果，我们从几何上描述了准拟概率分布为非负的状态集，并且可以将其视为假设一组有限结果中值的经典随机变量的联合分布。该集合是一个$（{ñ}^{\mathrm{2个}}-\mathrm{1个}）$的三维凸多面体 $ñ+\mathrm{1个}$ 顶点是唯一的纯状态， ${ñ}^{ñ+\mathrm{1个}}$ 高维面的数量，以及 ${ñ}^3（ñ+\mathrm{1个}）/\mathrm{2个}$ 边缘。