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arXiv · 1606.03615

A Gleason-type theorem for any dimension based on a gambling formulation of Quantum Mechanics

Alessio Benavoli·Alessandro Facchini·Marco Zaffalon
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Abstract

Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n = 2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should be excluded from consideration.

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Alessio Benavoli, Alessandro Facchini, Marco Zaffalon. 2016-06-11. A Gleason-type theorem for any dimension based on a gambling formulation of Quantum Mechanics. https://doi.org/10.1007/s10701-017-0097-0

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