Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices

@article{Benavoli2016QuantumMT,
  title={Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices},
  author={Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},
  journal={Physical Review A},
  year={2016},
  volume={94},
  pages={042106}
}
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… 

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