Quantum Logics and Quantum Measurements

Gianni Cassinelli, Enrico G. Beltrametti

Sylvia Pulmannová

Oľga Nánásiová, L’ubica Valášková, Viera Čerňanová

The present paper is devoted to modelling of a probability measure of logical connectives on a quantum logic via a G-map, which is a special map on it.We follow the work in which the probability of logical conjunction (AND), disjunction (OR), symmetric difference (XOR) and their negations for non-compatible propositions are studied.Now we study all remaining cases of G-maps on quantum logic, namely a probability measure of projections, of implications, and of their negations.We show that unlike classical (Boolean) logic, probability measures of projections on a quantum logic are not necessarilly pure projections.We indicate how it is possible to define a probability measure of implication using a G-map in the quantum logic, and then we study some properties of this measure which are different from a measure of implication in a Boolean algebra.Finally, we compare the properties of a G-map with the properties of a probability measure related to logical connectives on a Boolean algebra.

Leonardo Vanni, Roberto Laura

Amandeep Singh

In the present communication, I deal with the modelling of Generalized Parametric R-Norm Information measure in quantum logic. This information measure is extended to Joint and Conditional measure in quantum logic.

Gregg S. Jaeger