Leggett-Garg inequalities in the quantum field theory of neutrino oscillations

TL;DR

This paper explores how Leggett-Garg inequalities, which test quantum nonclassicality over time, are violated in neutrino oscillations within quantum field theory, revealing stronger violations than in quantum mechanics.

Contribution

It derives an exact flavor-mass uncertainty product and establishes it as an upper bound for inequality violations, linking temporal nonclassicality to quantum uncertainty.

Findings

Stronger violation of Leggett-Garg inequalities in quantum field theory compared to quantum mechanics.

Derived an exact flavor-mass uncertainty product as an upper bound for violations.

Established a time analog of Tsirelson's bound for temporal inequalities.

Abstract

We investigate Leggett-Garg temporal inequalities in flavor-mixing processes. We derive an exact flavor-mass uncertainty product and we establish that it is an upper bound to the violation of the inequalities. This finding relates temporal nonclassicality to quantum uncertainty and provides a time analog of the Tsirelson upper bound to the violation of the spatial Bell inequalities. By studying the problem both in the exact field-theoretical setting and in the limiting quantum mechanical approximation, we show that Leggett-Garg inequalities are violated more strongly in quantum field theory than in quantum mechanics.