In quantum mechanics, the probability distributions of position and momentum of a particle are normally not the marginals of a joint distribution, that is unless -- as shown by Wigner in 1932 -- negative probabilities are allowed. Since then, much theoretical work has been done to study negative probabilities; most of this work is about what those probabilities are. We suggest shifting the emphasis to what negative probabilities are for. In this connection, we introduce the framework of observation spaces. An observation space is a family $\mathcal S = \big\langle\mathcal P_i: i\in I\big\rangle$ of probability distributions sharing a common sample space in a consistent way; a grounding for $\mathcal S$ is a signed probability distribution $\mathcal P$ such that every $\mathcal P_i$ is a restriction of $\mathcal P$; and the grounding problem for $\mathcal S$ is the problem of describing the groundings for $\mathcal S$. We show that a wide variety of quantum scenarios can be formalized as observation spaces, and we solve the grounding problem for a number of quantum observation spaces. Our main technical result is a rigorous proof that Wigner's distribution is the unique signed probability distribution yielding the correct marginal distributions for position and momentum and all their linear combinations.

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负概率：它们是什么以及它们的用途

在量子力学中，粒子的位置和动量的概率分布通常不是联合分布的边缘，也就是说，除非——如 Wigner 在 1932 年所示——允许负概率。从那时起，人们做了很多研究负概率的理论工作。这项工作的大部分内容是关于这些概率是什么。我们建议将重点转移到负概率的用途上。在这方面，我们介绍了观察空间的框架。一个观察空间是一个族 $\mathcal S = \big\langle\mathcal P_i: i\in I\big\rangle$ 的概率分布以一致的方式共享一个公共样本空间；$\mathcal S$ 的基础是一个有符号概率分布 $\mathcal P$，使得每个 $\mathcal P_i$ 都是 $\mathcal P$ 的限制；而 $\mathcal S$ 的基础问题是描述 $\mathcal S$ 的基础的问题。我们展示了各种各样的量子场景可以被形式化为观察空间，并且我们解决了许多量子观察空间的基础问题。我们的主要技术结果是严格证明 Wigner 分布是唯一的有符号概率分布，为位置和动量及其所有线性组合产生正确的边际分布。