Information-reality complementarity: The role of measurements and quantum reference frames

Recently, a measure has been put forward which allows for the quantification of the degree of reality of an observable for a given preparation [Bilobran and 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.

Figure 1

(a) Generic state ${\rho }_{\mathcal{S}}\in {\mathcal{H}}_{\mathcal{A}}\otimes {\mathcal{H}}_{\mathcal{B}}$ becomes ${\mathcal{M}}_A^{\epsilon }\left({\rho }_{\mathcal{S}}\right)$ under monitoring of an observable $A$ acting on ${\mathcal{H}}_{\mathcal{A}}$. (b) Same process abstractly pictured in terms of irreality and information. As both local and global information is generated, the irreality of $A$ decreases [see Eq. (35)].