  Measurement incompatibility is one of the most striking examples of how
quantum physics is different from classical physics. Two measurements are
incompatible if they cannot arise via classical post-processing from a third
one. A natural way to quantify incompatibility is in terms of noise robustness.
In the present article, we review recent results on the maximal noise
robustness of incompatible measurements, which have been obtained by the
present authors using free spectrahedra, and rederive them using tensor norms.
In this way, we make them accessible to a broader audience from quantum
information theory and mathematical physics and contribute to the fruitful
interactions between Banach space theory and quantum information theory. We
also describe incompatibility witnesses using tensor norm and matrix convex set
duality, emphasizing the relation between the different notions of witnesses.
