# Measurement incompatibility and steering are necessary and sufficient for operational contextuality

## TL;DR

This paper demonstrates that measurement incompatibility and steering are both necessary and sufficient conditions for operational contextuality, linking these fundamental quantum phenomena.

## Contribution

It establishes a precise equivalence between measurement incompatibility, steering, and operational contextuality in quantum theory.

## Key findings

- Measurement incompatibility is necessary and sufficient for contextuality.
- Steering is necessary and sufficient for contextuality.
- Provides a new approach to problems in measurement incompatibility and steering.

## Abstract

Contextuality is a signature of operational nonclassicality in the outcome statistics of an experiment. This notion of nonclassicality applies to a breadth of physical phenomena. Here, we establish its relation to two fundamental nonclassical entities in quantum theory; measurement incompatibility and steering. We show that each is necessary and sufficient the failure of operational contextuality. We exploit the established connection to contextuality to provide a novel approach to problems in measurement incompatibility and steering.