It is sometimes stated that Gleason’s theorem prevents the construction of hidden-variable models for quantum entities described in a more than twodimensional Hilbert space. In this paper however we explicitly construct a classical (macroscopical) system that can be represented in a threedimensional real Hilbert space, the probability structure appearing as the result of a lack of knowledge about the measurement context. We briefly discuss Gleason’s theorem from this point of view.

Diederik Aerts

Bob Coecke

Bart D'Hooghe

A mechanistic macroscopic physical entity with a three-dimensional Hilbert space description

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