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

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