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Recently, inspired by Einstein-Podolsky-Rosen's notion of elements ofreality, Bilobran and Angelo gave a formal and operational characterization of(ir)reality [EPL 112, 40005 (2015)]. From this approach, the authors were ableto define a measure of (ir)realism, or (in)definiteness, of an observable givena preparation of a quantum system. As well, in [Phys. Rev. A 97, 022107(2018)], Dieguez and Angelo studied the variation of reality of observables byintroducing a map, called monitoring, through weak projective non-revealedmeasurements. The authors showed that an arbitrary-intensity unrevealedmeasurement of a given observable $X$ generally increases its reality, alsoincreasing the reality of its incompatible observables $X'$. However, fromthese results, natural questions arise: under the monitoring map of $X$, howmuch does the reality of $X'$ increase in comparison to that of $X$? Does italways 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, themonitoring map of $X$ does not affect the already established reality of $X'$,even when they are maximally incompatible. On the other hand, there arecircumstances where the variation of reality of both observables is the same,even when they are maximally incompatible. Besides, we give a quantum circuitto implement the monitoring map and use it to experimentally verify thevariation of reality of observables using IBM's quantum computers.

Reality variation under monitoring with weak measurements