# Ambiguous measurements, signalling and violations of Leggett-Garg inequalities

## TL;DR

This paper explores how ambiguous quantum measurements affect tests of Leggett-Garg inequalities, proposing new assumptions and an experiment demonstrating violation of LGIs while satisfying signalling constraints.

## Contribution

It introduces a new assumption equating invasive influences of ambiguous and unambiguous measurements and demonstrates a quantum-optics experiment violating LGIs under these conditions.

## Key findings

- Ambiguous measurements can bypass non-invasive measurability assumptions.
- A new signalling condition is derived for the plausibility of LG tests.
- An experiment with a three-level system violates LGIs while satisfying signalling constraints.

## Abstract

Ambiguous measurements do not reveal complete information about the system under test. Their quantum-mechanical counterparts are semi-weak (or in the limit, weak-) measurements and here we discuss their role in tests of the Leggett-Garg inequalities. We show that, whilst ambiguous measurements allow one to forgo the usual non-invasive measureability assumption, to derive an LGI that may be violated, we are forced to introduce another assumption that equates the invasive influence of ambiguous and unambiguous detectors. Based on this assumption, we derive signalling conditions that should be fulfilled for the plausibility of the Leggett-Garg test. We then propose an experiment on a three-level system with a direct quantum-optics realisation that satisfies all signalling constraints and violates a Leggett-Garg inequality.