# Device-independent tests of structures of measurement incompatibility

## TL;DR

This paper develops device-independent methods to certify the structure of measurement incompatibility in quantum systems, demonstrating that certain Bell inequality violations can reveal specific incompatibility structures without trusting the measurement devices.

## Contribution

It introduces a framework for device-independent certification of measurement incompatibility structures using Bell inequalities and extends these results to EPR-steering scenarios.

## Key findings

- Correlations from local measurements violate limits set by compatibility assumptions.
- Quantum correlations demonstrate genuine triplewise incompatibility in a device-independent manner.
- Results apply to both quantum and nonsignaling models, broadening their applicability.

## Abstract

In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they can not be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell nonlocality. This makes of crucial importance developing tools for certifying whether a set of measurements posses a certain structure of incompatibility. Here we show that, for quantum or nonsignaling models, if the measurements employed in a Bell test satisfy a given type of compatibility, then the amount of violation of some specific Bell inequalities become limited. Then, we show that correlations arising from local measurements on two-qubit states violate these limits, which rules out in a device-independent way such structures of incompatibility. In particular, we prove that quantum correlations allow for a device-independent demonstration of genuine triplewise incompatibility. Finally, we translate these results into a semi-device-independent Einstein-Podolsky-Rosen-steering scenario.