Negative probabilities: What they are and what they are for

Abstract

An observation space $\mathcal{S}$ is a family of probability distributions $⟨P_i:i\in I⟩$ sharing a common sample space $\Omega$ in a consistent way. A \emph{grounding} for $\mathcal{S}$ is a signed probability distribution $\mathcal{P}$ on $\Omega$ yielding the correct marginal distribution $P_i$ 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.

This article supersedes arXiv:1502.00666 and arXiv:1807.10382

References in corpus (2)

• Efficient computation of the Zassenhaus formula
• A Sober Look at Spectral Learning

Cited by in corpus (1)

• Overdrawing Urns using Categories of Signed Probabilities