A hidden measurement representation for quantum entities described by finite-dimensional complex Hilbert spaces

Abstract

It will be shown that the probability calculus of a quantum mechanical entity can be obtained in a deterministic framework, embedded in a real space, by introducing a lack of knowledge in the measurements on that entity. For all n ∃ ℕ we propose an explicit model in\(\mathbb{R}^{n^2 } \), which entails a representation for a quantum entity described by an n-dimensional complex Hilbert space þn, namely, the “þn,Euclidean hidden measurement representation.” This Euclidean hidden measurement representation is also in a more general sense equivalent with the orthodox Hilbert space formulation of quantum mechanics, since every mathematical ingredient of ordinary quantum mechanics can easily be translated into the framework of these representations.