Reformulation of the hidden variable problem using entropic measure of uncertainty

Miklós Rédei

pp. 371-379

in: Synthese 73 (2), 1987.

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.