  Recently, inspired by Einstein-Podolsky-Rosen's notion of elements of
reality, Bilobran and Angelo gave a formal and operational characterization of
(ir)reality [EPL 112, 40005 (2015)]. From this approach, the authors were able
to define a measure of (ir)realism, or (in)definiteness, of an observable given
a preparation of a quantum system. As well, in [Phys. Rev. A 97, 022107
(2018)], Dieguez and Angelo studied the variation of reality of observables by
introducing a map, called monitoring, through weak projective non-revealed
measurements. The authors showed that an arbitrary-intensity unrevealed
measurement of a given observable $X$ generally increases its reality, also
increasing the reality of its incompatible observables $X'$. However, from
these results, natural questions arise: under the monitoring map of $X$, how
much does the reality of $X'$ increase in comparison to that of $X$? Does it
always increase? This is the kind of question we address in this article.
Surprisingly, we show that it is possible that the variation of the reality of
$X'$ is bigger than the variation of the reality of $X$. As well, the
monitoring map of $X$ does not affect the already established reality of $X'$,
even when they are maximally incompatible. On the other hand, there are
circumstances where the variation of reality of both observables is the same,
even when they are maximally incompatible. Besides, we give a quantum circuit
to implement the monitoring map and use it to experimentally verify the
variation of reality of observables using IBM's quantum computers.
