The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem |
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Authors: | Diederik Aerts Massimiliano Sassoli de Bianchi |
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Affiliation: | 1. Center Leo Apostel for Interdisciplinary Studies and Department of Mathematics, Brussels Free University, Brussels, Belgium;2. Laboratorio di Autoricerca di Base, 6914 Lugano, Switzerland |
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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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Keywords: | Measurement problem Hidden-variable Hidden-measurement Quantum decoherence SU(N) |
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