[en] Given two unital C-algebras A, B and their state spaces E /sub A/, E /sub B/ respectively, (A, E /sub A/) is said to have (B, E /sub B/) as a hidden theory via a linear, positive, unitpreserving map L: B-A if, for all /phi/εE /sub A/, L/phi/ can be decomposed in E /sub B/ into states with pointwise strictly less dispersion than that of /phi/. Conditions on A and L are found that exclude (A, E /sub A/) from having a hidden theory via L. It is shown in particular that, if A is simple, then no (B, E /sub B/) can be a hidden theory of (A, E /sub E/) via a Jordan homomorphism; it is proved furthermore that, if A is a UHF algebra, it cannot be embedded into a large C-algebra B such that (B, E /sub B/) is a hidden theory of (A, E /sub A/) via a conditional expectation from B onto A