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arXiv · 1404.2429

The Extended Bloch Representation of Quantum Mechanics and the Hidden-Measurement Solution to the Measurement Problem

Diederik Aerts·Massimiliano Sassoli de Bianchi
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Abstract

A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement.

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Diederik Aerts, Massimiliano Sassoli de Bianchi. 2014-04-09. The Extended Bloch Representation of Quantum Mechanics and the Hidden-Measurement Solution to the Measurement Problem. https://doi.org/10.1016/j.aop.2014.09.020

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