Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco
(2017)
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A Gleason-type theorem for any dimension based on a gambling formulation of Quantum Mechanics.
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*Foundations of Physics*, 47.
pp. 991-1002.

## 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.

Item Type: | Scientific journal article, Newspaper article or Magazine article |
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Subjects: | Physical sciences > Physics > Quantum mechanics Mathematical sciences > Statistics > Probability |

Department/unit: | Dipartimento tecnologie innovative > Istituto Dalle Molle di studi sullâ€™intelligenza artificiale USI-SUPSI |

Depositing User: | Alessandro Facchini |

Date Deposited: | 24 Aug 2023 13:32 |

Last Modified: | 24 Aug 2023 13:32 |

URI: | http://repository.supsi.ch/id/eprint/14584 |

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