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Kochen-Specker theorem for von Neumann algebras
The Kochen-Specker theorem has been discussed intensely ever since its
original proof in 1967. It is one of the central no-go theorems of quantum
theory, showing the non-existence of a certain kind of hidden states models. In
this paper, we first offer a new, non-combinatorial proof for quantum systems
with a type factor as algebra of observables, including .
Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von
Neumann algebra without summands of types and ,
using a known result on two-valued measures on the projection lattice
. Some connections with presheaf formulations as proposed by
Isham and Butterfield are made.Comment: 22 pages, no figure
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