Abstract
Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, ℬ, E(A), E(ℬ) are von Neumann algebras and their state spaces respectively, (ℬ, E(ℬ)) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from ℬ onto A if for all states φ ε E(A) the composite state φ ° L ε E(ℬ) can be obtained as an average over states in E(ℬ) that have smaller entropic uncertainty than the entropic uncertainty of φ. It is shown that if L is a Jordan homomorphism then (ℬ, E(ℬ)) is not an entropic hidden theory of (A, E(A)) via L.
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Rédei, M. Reformulation of the hidden variable problem using entropic measure of uncertainty. Synthese 73, 371–379 (1987). https://doi.org/10.1007/BF00484748
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DOI: https://doi.org/10.1007/BF00484748