Bounding the quantum dimension with contextuality
We show that quantum contextuality is a resource that can be used to certify the dimension of quantum systems. To prove this, we derive the bounds for different dimensions and scenarios of the simplest noncontextuality inequalities. The resulting dimension witnesses work independently of the prepared quantum state. Our constructions are robust against noise and imperfections, and we show that a recent experiment can be viewed as an implementation of a state-independent quantum dimension witness.