Modeling Leggett-Garg-inequality violation

TL;DR

This paper develops an operational model to systematically attribute violations of the Leggett-Garg inequality to invasiveness, using a controllable parameter linked to the measurability of the system, thus clarifying the quantum-classical boundary.

Contribution

It introduces a new dimensional independent invasiveness model that quantifies measurement effects through a controllable parameter, advancing understanding of Leggett-Garg inequality violations.

Findings

Model allows systematic attribution of violations to invasiveness

Parameter linked to measurability controls measurement effects

Provides a framework for generalized measurements and back action

Abstract

The Leggett-Garg inequality is a widely used test of the "quantumness" of a system, and involves correlations between measurements realized at different times. According to its widespread interpretation, a violation of the Legget-Garg inequality disproofs macroscopic realism and non-invasiveness. Nevertheless, recent results point out that macroscopic realism is a model dependent notion and that one should always be able to attribute to invasiveness a violation of a Legget-Garg inequality. This opens some natural questions: how to provide such an attribution in a systematic way? How can apparent macroscopic realism violation be recast into a dimensional independent invasiveness model? The present work answers these questions by introducing an operational model where the effects of invasiveness are controllable through a parameter associated with what is called the {\it measurability} of the physical system. Such a parameter leads to different generalized measurements that can be associated with the dimensionality of a system, to measurement errors or to back action.