Neither weak nor strong entropic Leggett-Garg inequalities can be violated

TL;DR

This paper demonstrates that both strong and weak entropic Leggett-Garg inequalities cannot be violated by quantum measurements, reinforcing the classical-quantum boundary and clarifying the limitations of quantum violations.

Contribution

It introduces and analyzes entropic Leggett-Garg inequalities, showing they cannot be violated by quantum measurements, unlike some standard inequalities, thus clarifying the classical-quantum boundary.

Findings

Entropic inequalities cannot be violated by strong quantum measurements.

Weak entropic inequalities also cannot be violated, even with unprojected systems.

Quantum mechanics describes classical devices accurately, but not necessarily the quantum system itself.

Abstract

The Leggett-Garg inequalities probe the classical-quantum boundary by putting limits on the sum of pairwise correlation functions between classical measurement devices that consecutively measured the same quantum system. The apparent violation of these inequalities by standard quantum measurements has cast doubt on quantum mechanics' ability to consistently describe classical objects. Recent work has concluded that these inequalities cannot be violated by either strong or weak projective measurements [1]. Here I consider an entropic version of the Leggett-Garg inequalities that are different from the standard inequalities yet similar in form, and can be defined without reference to any particular observable. I find that the entropic inequalities also cannot be be violated by strong quantum measurements. The entropic inequalities can be extended to describe weak quantum measurements, and I show that these weak entropic Leggett-Garg inequalities cannot be violated either even though the quantum system remains unprojected, because the inequalities describe the classical measurement devices, not the quantum system. I conclude that quantum mechanics adequately describes classical devices, and that we should be careful not to assume that the classical devices accurately describe the quantum system.