2001/11/13 by Diederik Aerts, Bob Coecke, Bart D'Hooghe +1
Physics and Astronomy · #quant-ph
published as Helvetica Physica Acta, 70, 793, 1997 · 11 pages, 5 figures
arxiv created 2001/11/13 · arxiv updated 2009/12/01
It is sometimes stated that Gleason's theorem prevents the construction of hidden-variable models for quantum entities described in a more than two-dimensional Hilbert space. In this paper however we explicitly construct a classical (macroscopical) system that can be represented in a three-dimensional 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.