Optimal violation of Leggett-Garg inequality for arbitrary spin and emergence of classicality through unsharp measurement

TL;DR

This paper demonstrates that the Leggett-Garg inequality can be maximally violated for particles of any spin, and shows how classical behavior emerges through unsharp measurements, linking inequality satisfaction to macroscopic realism.

Contribution

It extends the maximal violation of the Leggett-Garg inequality to arbitrary spin systems and explores the emergence of classicality via unsharp measurement schemes.

Findings

Maximal violation of Leggett-Garg inequality for any spin value.

Classicality emerges below a specific unsharpness threshold.

Leggett-Garg inequality satisfaction is necessary and sufficient for macroscopic realism.

Abstract

We consider temporal correlations of particles with arbitrary spin. We show that the Leggett-Garg inequality can be maximally violated irrespective of the value of spin, thus improving upon an earlier result by Kofler and Brukner [Phys. Rev. Lett. \textbf{99}, 180403 (2007)]. Our proof is accomplished through a suitable adoption of a measurement scheme which has previously been employed for studying the spatial correlation in a system with arbitrary spin. We next consider generalized or unsharp measurements as a method for coarse graining in a quantitative manner, and show that classicality emerges below a precise value of the sharpness parameter. Satisfaction of the Leggett-Garg inequality is shown to be a necessary and sufficient condition for macroscopic realism.