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Summary: A mechanistic macroscopic physical entity with a
three-dimensional Hilbert space description
Diederik Aerts, Bob Coecke, Bart D'Hooghe and Frank Valckenborgh
Center Leo Apostel (CLEA) and
Foundations of the Exact Sciences (FUND),
Brussels Free University,
Pleinlaan 2, B1050, Brussels.
diraerts@vub.ac.be, bocoecke@vub.ac.be,
bdhooghe@easynet.be, fvalcken@vub.ac.be
Abstract
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.
1 Introduction
Even after more than 60 years there remain many problems on the 'understand-
ing' of quantum mechanics. From the early days, a main concern of the majority
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