Negative probabilities: What they are and what they are for

• URL: http://arxiv.org/abs/2009.10552v2
• Date: Wed, 30 Mar 2022 15:57:45 GMT
• Title: Negative probabilities: What they are and what they are for
• Authors: Andreas Blass and Yuri Gurevich
• Abstract summary: An observation space $mathcal S$ is a family of probability distributions $langle P_i: iin I rangle$ sharing a common sample space $Omega$ in a consistent way. A emphgrounding for $mathcal S$ is a signed probability distribution $mathcal P$ on $Omega$ yielding the correct marginal distribution $P_i$ for every $i$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An observation space $\mathcal S$ is a family of probability distributions $\langle P_i: i\in I \rangle$ 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.

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