Generalized Kochen-Specker Theorem

Details Generalized Kochen-Specker Theorem Generalized Kochen-Specker Theorem

1995-10-19

arxiv.org/abs/quant-ph/9510018v1

Found.Phys. 26 (1996) 807-812

Physics

Quantum Physics

7 pages, LaTeX, to appear in Foundations of Physics (1996)

Scientific paper

10.1007/BF02058634

A generalized Kochen-Specker theorem is proved. It is shown that there exist sets of $n$ projection operators, representing $n$ yes-no questions about a quantum system, such that none of the $2^n$ possible answers is compatible with sum rules imposed by quantum mechanics. Namely, if a subset of commuting projection operators sums up to a matrix having only even or only odd eigenvalues, the number of ``yes'' answers ought to be even or odd, respectively. This requirement may lead to contradictions. An example is provided, involving nine projection operators in a 4-dimensional space.

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