Reformulation of the hidden variable problem using entropic measure of uncertainty

Synthese 73 (2):371 - 379 (1987)
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, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from onto A if for all states E(A) the composite state ° L E() can be obtained as an average over states in E() that have smaller entropic uncertainty than the entropic uncertainty of . It is shown that if L is a Jordan homomorphism then (, E()) is not an entropic hidden theory of (A, E(A)) via L.
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DOI 10.1007/BF00484748
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Arthur Fine (1980). Correlations and Physical Locality. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:535 - 562.

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