# Leggett-Garg tests of macrorealism: checks for non-invasiveness and generalizations to higher-order correlators

## TL;DR

This paper proposes a modified measurement protocol for Leggett-Garg tests that ensures non-invasiveness from both classical and quantum viewpoints, enabling more reliable tests of macrorealism and extending to higher-order correlations.

## Contribution

It introduces a new non-invasive measurement protocol for Leggett-Garg tests and generalizes the framework to higher-order correlation functions.

## Key findings

- The protocol can be experimentally checked for non-invasiveness.
- Extension to higher-order correlation functions is demonstrated.
- New conditions for macrorealism are derived.

## Abstract

In the tests for macrorealism proposed by Leggett and Garg, the temporal correlation functions of a dichotomic variable Q must be measured in a non-invasive way to rule out alternative classical explanations of Leggett-Garg inequality violations. Ideal negative measurements, in which a null result is argued to be a non-invasive determination of the system's state, are often used. From a quantum-mechanical perspective, such a measurement collapses the wave function and will therefore typically be found to be invasive under any experimental check. Here, a simple modified ideal negative measurement protocol is described for measuring the correlation functions which is argued to be non-invasive from both classical and quantum perspectives and hence the non-invasiveness can then be checked experimentally, thereby permitting a quantitative measure of the degree of clumsiness of the measurement. It is also shown how this procedure may be extended to measure higher-order correlation functions and a number of higher-order conditions for macrorealism are derived.