@conference{Benavoli2017m,
title = {Bayes + Hilbert = Quantum Mechanics},
author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco },
url = {http://qpl.science.ru.nl/papers/QPL_2017_paper_4.pdf},
year = {2017},
date = {2017-07-05},
booktitle = {Proceedings of the 14th International Conference on Quantum Physics and Logic (QPL 2017), Nijmegen, The Netherlands, 3-7 July},
keywords = {Quantum mechanics},
pubstate = {published},
tppubtype = {conference}
}

@article{benavoli2016f,
title = {A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics},
author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco},
url = {http://arxiv.org/abs/1606.03615},
doi = {10.1007/s10701-017-0097-0},
issn = {1572-9516},
year = {2017},
date = {2017-01-01},
journal = {Foundations of Physics},
volume = {47},
number = {7},
pages = {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.},
keywords = {Quantum mechanics},
pubstate = {published},
tppubtype = {article}
}

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.

@article{benavoli2016d,
title = {Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices},
author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco},
url = {http://arxiv.org/abs/1605.08177
},
doi = {10.1103/PhysRevA.94.042106},
year = {2016},
date = {2016-10-01},
journal = {Physics Review A},
volume = {94},
pages = {042106},
publisher = {American Physical Society},
abstract = {We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.},
keywords = {Quantum mechanics},
pubstate = {published},
tppubtype = {article}
}

We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.