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We quantify the intrinsic noise content of an observable in a generalprobabilistic theory and derive a noise content inequality for incompatibleobservables. We apply the derived inequality to standard quantum theory, thequantum theory of processes, and polytope state spaces. The noise content forpositive operator-valued measures takes a particularly simple form and equalsthe sum of minimal eigenvalues of all the effects. We illustrate our findingswith a number of examples including the introduced notion of reverseobservables.

A necessary condition for incompatibility of observables in general probabilistic theories