# Robust self-testing of quantum systems via noncontextuality inequalities

## TL;DR

This paper introduces a new method for self-testing quantum systems using non-contextuality inequalities, combining graph theory and optimization to ensure unique solutions and demonstrate robustness in key inequalities.

## Contribution

It presents a novel scheme that leverages graph-theoretic and optimization tools for robust self-testing of quantum systems via non-contextuality inequalities.

## Key findings

- Demonstrates robust self-testing for the Klyachko-Can-Biniciogglu-Shumovsky inequality.
- Extends self-testing to contextuality scenarios with odd n-cycle compatibility.
- Utilizes a graph-theoretic framework combined with mathematical optimization.

## Abstract

Characterising unknown quantum states and measurements is a fundamental problem in quantum information processing. In this Letter, we provide a novel scheme to self-test local quantum systems using non-contextuality inequalities. Our work leverages the graph-theoretic framework for contextuality introduced by Cabello, Severini, and Winter, combined with tools from mathematical optimisation that guarantee the unicity of optimal solutions. As an application, we show that the celebrated Klyachko-Can-Biniciogglu-Shumovsky inequality and its generalisation to contextuality scenarios with odd n-cycle compatibility relations admit robust self-testing.