The Logic of Quantum Measurements

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.

Sylvia Pulmannová

Masahito Ueda

A quantum measurement is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and from the outcome of the measurement. This paper analyzes why many quantum measurements are logically irreversible, shows how to make them logically reversible, and discusses reversing measurement that returns the postmeasurement state to the premeasurement state by another measurement (physical reversibility). Reversing measurement and unitarily reversible quantum operation are compared from the viewpoint of error correction in quantum computation.

Dan Cristian Marinescu, Gabriela M. Marinescu

M. Ueda

A quantum measurement is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and from the outcome of the measurement. This paper analyzes why many quantum measurements are logically irreversible, shows how to make them logically reversible, and discusses reversing measurement that returns the postmeasurement state to the premeasurement state by another measurement (physical reversibility). Reversing measurement and unitarily reversible quantum operation are compared from the viewpoint of error correction in quantum computation. 1.

Michael B. Mensky