Negative probabilities: what are they for? * *Partially supported by the US Army Research Office under W911NF-20-1-0297.

Abstract

An observation space is a family of probability distributions sharing a common sample space Ω in a consistent way. A grounding for is a signed probability distribution on Ω yielding the correct marginal distribution 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.