# Paths, negative "probabilities", and the Leggett-Garg inequalities

## TL;DR

This paper analyzes how measurement choices influence future outcomes in quantum systems, showing that negative probabilities are more reliable indicators of signaling in time than Leggett-Garg inequalities.

## Contribution

It introduces a path-based analysis of signaling in time and compares the effectiveness of negative probabilities versus Leggett-Garg inequalities as witnesses.

## Key findings

- Signaling in time occurs when measurements destroy interference between paths.
- Negative probabilities serve as a more reliable witness of signaling than Leggett-Garg inequalities.
- Both methods can fail under certain conditions.

## Abstract

We present a path analysis of the condition under which the outcomes of previous observation affect the results of the measurements yet to be made. It is shown that this effect, also known as "signalling in time", occurs whenever the earlier measurements are set to destroy interference between two or more virtual paths. We also demonstrate that Feynman's negative "probabilities" provide for a more reliable witness of "signalling in time", than the Leggett-Garg inequalities, while both methods are frequently subject to failure