More on the state-dependent implication in quantum mechanics (vol 27, pg 7503, 1994)

The mixing structure of a given quantum state (statistical operator) rho is considered, that is, the pure states and associated weights of which it consists. Its influence on the state-dependent quantum logical implication determined by rho is also studied. It is found that it has no influence at all except through the null-projector. It is shown that the latter, when it determines the state-dependent implication, in a certain sense, carries with it all the Boolean mathematical structure of projectors in the given Boolean subalgebra a of quantum logic P(H), where B is the 'domain' of definition of the state-dependent implication.