  Recently, a measure has been put forward which allows for the quantification
of the degree of reality of an observable for a given preparation [A. L. O.
Bilobran and R. M. Angelo, Europhys. Lett. 112, 40005 (2015)]. Here we employ
this quantifier to establish, on formal grounds, relations among the concepts
of measurement, information, and physical reality. After introducing
mathematical objects that unify weak and projective measurements, we study
scenarios showing that an arbitrary-intensity unrevealed measurement of a given
observable generally leads to an increase of its reality and also of its
incompatible observables. We derive a complementarity relation connecting an
amount of information associated with the apparatus with the degree of
irreality of the monitored observable. Specifically for pure states, we show
that the entanglement with the apparatus precisely determines the amount by
which the reality of the monitored observable increases. We also point out some
mechanisms whereby the irreality of an observable can be generated. Finally,
using the aforementioned tools, we construct a consistent picture to address
the measurement problem.
