Foundations of non-commutative probability theory (Extended abstract)

• URL: http://arxiv.org/abs/2306.01131v1
• Date: Thu, 1 Jun 2023 20:34:01 GMT
• Title: Foundations of non-commutative probability theory (Extended abstract)
• Authors: Daniel Lehmann
• Abstract summary: Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way.
• Score: 1.8782750537161614
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way.The mystery presented by the algebraic equations satisfied by (non-commuting) observables that cannot be observed in the same states is elucidated.

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