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

Abstract

We consider the problem of gambling on a quantum experiment and enforce rational behaviour 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 generalised to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalised 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), marginalisation (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.

This paper has been accepted to Physics Review A

References in corpus (3)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Quantum Mechanics as Quantum Information (and only a little more)
• Symmetric Informationally Complete Measurements of Arbitrary Rank

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• On testing the simulation theory
• An information and field theoretic approach to the grand canonical ensemble
• Computational Complexity and the Nature of Quantum Mechanics
• Computational Complexity and the Nature of Quantum Mechanics (Extended version)
• Quantum indistinguishability through exchangeable desirable gambles