Fragile systems: A hidden-variable Bayesian framework leading to quantum theory

TL;DR

This paper derives quantum theory from a Bayesian framework applied to fragile systems, explaining non-classical phenomena through hidden variables and linear algebra, bridging classical and quantum descriptions.

Contribution

It introduces a novel derivation of quantum mechanics from Bayesian probability applied to fragile systems, highlighting the emergence of quantum features from classical probabilities.

Findings

Quantum states as states of knowledge in Bayesian framework

Non-commutativity arises naturally from integral equations

Classical limit corresponds to non-fragile, commutative measurements

Abstract

An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still a challenge at the foundations of our description of physical phenomena. Among some proposals, the idea that quantum states are essentially states of knowledge in a Bayesian framework is an intriguing possibility due to its explanatory power. In this work, the formalism of quantum theory is derived from the application of Bayesian probability theory to "fragile" systems, that is, systems that are perturbed by the measurement. Complex Hilbert spaces, non-commuting operators and the trace rule for expectations all arise naturally from the use of linear algebra to solve integral equations involving classical probabilities over hidden variables. The non-fragile limit of the theory, where all measurements are commutative and the theory becomes analogous to classical statistical theory is discussed as well.