# Leggett-Garg macrorealism and the quantum nondisturbance conditions

## TL;DR

This paper explores the connection between Leggett-Garg macrorealism, NSIT conditions, and quantum nondisturbance, providing a unified framework to test macrorealist theories and tighten loopholes using hierarchical tests.

## Contribution

It establishes the equivalence between NSIT conditions and quantum nondisturbance criteria, extending previous methods and proposing a hierarchy of tests to better disprove macrorealist theories.

## Key findings

- NSIT conditions are satisfied iff certain measurement compatibility criteria are met.
- A hierarchical framework tightens the macrorealism loophole.
- Structural results support a unified approach to macrorealism testing.

## Abstract

We investigate the relation between a refined version of Leggett and Garg conditions for macrorealism, namely the no-signaling-in-time (NSIT) conditions, and the quantum mechanical notion of nondisturbance between measurements. We show that all NSIT conditions are satisfied for any state preparation if and only if certain compatibility criteria on the state-update rules relative to the measurements, i.e. quantum instruments, are met. The systematic treatment of NSIT conditions supported by structural results on nondisturbance provides a unified framework for the discussion of the the clumsiness loophole. This extends previous approaches and allows for a tightening of the loophole via a hierarchy of tests able to disprove a larger class of macrorealist theories. Finally, we discuss perspectives for a resource theory of quantum mechanical disturbance related to violations of macrorealism.