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

TL;DR

This paper explores the relationship between measurement, information, and reality in quantum systems, introducing a measure of an observable's reality and analyzing how measurements influence it, especially in pure states and with quantum reference frames.

Contribution

It formalizes the connection between measurement and reality using a new quantifier, unifies weak and projective measurements, and addresses the measurement problem in quantum mechanics.

Findings

Unrevealed measurements can increase the reality of an observable.

Entanglement with the measurement apparatus determines the increase in reality.

A complementarity relation links information and irreality of observables.

Abstract

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.