# Probing inequivalent forms of Legget-Garg inequality in subatomic systems

## TL;DR

This paper compares different forms of Leggett-Garg inequalities in subatomic systems, showing their experimental feasibility, energy-dependent violations, and effects of decoherence on quantum nonclassicality.

## Contribution

It analyzes Wigner and Clauser-Horne forms of LGI in neutrino and meson systems, highlighting their measurement advantages and energy-dependent violations.

## Key findings

- Wigner and Clauser-Horne LGIs are more experimentally accessible for neutrinos.
- Maximum quantum violations occur near neutrino flux peaks.
- Decoherence reduces violation levels in meson systems.

## Abstract

We study various formulations of Leggett-Garg inequality (LGI), specifically, the Wigner and Clauser-Horne forms of LGI, in the context of subatomic systems, in particular, three flavor neutrino as well as meson systems. The optimal forms of various LGIs for either neutrinos or mesons are seen to depend on measurement settings. For the neutrinos, some of these inequalities can be written completely in terms of experimentally measurable probabilities. Hence, the Wigner and Clauser-Horne forms of LGI are found to be more suitable as compared to the standard LGI from the experimental point of view for the neutrino system. Further, these inequalities exhibit maximum quantum violation around the energies roughly corresponding to the maximum neutrino flux. The Leggett-Garg type inequality is seen to be more suited for the meson dynamics. The meson system being inherently a decaying system, allows one to see the effect of decoherence on the extent of violation of various inequalities. Decoherence is observed to reduce the degree of violation, and hence the nonclassical nature of the system.