On the problem of local hidden variables in algebraic quantum mechanics
MiklΓ³s RΓ©dei Β· Journal of Mathematical Physics Β· 1987
Given two Bose-type quasilocal C*-algebras π, β¬, their state spaces E(π), E(β¬), and a positive, unit preserving map L: β¬βπ, respecting the local structure of π and β¬ (π,E(π)) is said to have (β¬,E(β¬)) as a local hidden theory via L if for all states Ο in E(π), L*Ο can be decomposed in E(β¬) via a subcentral measure into states with pointwise strictly less dispersion than the dispersion of Ο. After motivating this definition of local hidden theory it is shown that if, in addition, L factorizes on disjoint local algebras, then (β¬, E(β¬)) is not a local hidden theory of (π,E(π)) via L.