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On state-dependent implication in quantum mechanics. (English) Zbl 0843.03039
Summary: This paper studies a generalization of a priori implication $E\le F$, meaning of course $EF=E$, in the quantum logic $𝒫\left(ℋ\right)$ of all projectors. The new definition can be applied also to new pairs of events, being based on the indistinguishability of some events when considered from the standpoint of a (fixed) state $\rho$. The mathematical theory of factor Boolean algebras, on which this extension is based, is clarified.

##### MSC:
 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic
##### Keywords:
quantum logic; projectors; factor Boolean algebras