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.
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