Reality variation under monitoring with weak measurements

TL;DR

This paper investigates how weak measurements, called monitoring, affect the reality of quantum observables, revealing surprising behaviors and providing an experimental implementation on IBM quantum computers.

Contribution

It introduces a detailed analysis of reality variation under monitoring, showing that reality changes can be counterintuitive and providing a quantum circuit for experimental verification.

Findings

Reality variation of incompatible observables can differ significantly.

Monitoring can increase the reality of one observable without affecting another.

Experimental verification was successfully performed on IBM quantum computers.

Abstract

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.