# Negative probabilities: What they are and what they are for

arXiv: https://arxiv.org/abs/2009.10552 · HTML: https://mlsanity.com/paper/2009.10552/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [Overdrawing Urns using Categories of Signed Probabilities](https://mlsanity.com/paper/2312.12453/) (2023)

## Abstract (arXiv)

An observation space mathcal S is a family of probability distributions langle Pi: i∈ I rangle sharing a common sample space Omega in a consistent way. A grounding for mathcal S is a signed probability distribution mathcal P on Omega yielding the correct marginal distribution Pi for every i. A wide variety of quantum scenarios can be formalized as observation spaces. We describe all groundings 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.