# Noise-disturbance relation and the Galois connection of quantum measurements

## TL;DR

This paper explores the fundamental noise-disturbance relationship in quantum measurements using Galois connections, introducing the concept of information leak and comparing it with joint measurability and simulability.

## Contribution

It introduces a Galois connection framework to analyze noise and disturbance, defining a new notion of information leak and comparing it with existing concepts in quantum measurement theory.

## Key findings

- Defined the leak of information as a closure map in the Galois framework
- Provided a physical interpretation of the information leak
- Compared leak with joint measurability and simulability concepts

## Abstract

The relation between noise and disturbance is investigated within the general framework of Galois connections. Within this framework, we introduce the notion of leak of information, mathematically defined as one of the two closure maps arising from the observable-channel compatibility relation. We provide a physical interpretation for it, and we give a comparison with the analogous closure maps associated with joint measurability and simulability for quantum observables.