  A robustness measure for incompatibility of quantum devices in the lines of
the robustness of entanglement is proposed. The concept of general robustness
measures is first introduced in general convex-geometric settings and these
ideas are then applied to measure how incompatible a given pair of quantum
devices is. The robustness of quantum incompatibility is calculated in three
special cases: a pair of Fourier-coupled rank-1 sharp observables, a pair of
decodable channels, where decodability means left-invertibility by a channel,
and a pair consisting of a rank-1 sharp observable and a decodable channel.
