No-signaling-in-time as a condition for macrorealism: the case of neutrino oscillations

TL;DR

This paper investigates the conditions for macrorealism in neutrino oscillations, focusing on no-signaling-in-time and Leggett--Garg inequalities, revealing their relationships and limitations in different models.

Contribution

It compares no-signaling-in-time and Leggett--Garg inequalities in neutrino oscillations, highlighting their implications and differences in various theoretical frameworks.

Findings

Fulfillment of no-signaling-in-time implies Leggett--Garg inequalities are satisfied.

Leggett--Garg inequalities can be satisfied even when no-signaling-in-time is violated.

No-signaling-in-time is violated at distances longer than the coherence length in wave packet models.

Abstract

We consider two necessary and sufficient conditions for macrorealism recently appeared in the literature, known as no-signaling-in-time and arrow-of-time conditions, respectively, and study them in the context of neutrino flavor transitions, within both the plane wave description and the wave packet approach. We then compare the outcome of the above investigation with the implication of various formulations of Leggett--Garg inequalities. In particular, we show that the fulfillment of the addressed conditions for macrorealism in neutrino oscillations implies the fulfillment of Leggett--Garg inequalities, whereas the converse is not true. Finally, in the framework of wave packet approach, we also prove that, for distances longer than the coherence length, the no-signaling-in-time condition is always violated whilst Leggett--Garg inequalities are not.