  We consider pairs of quantum observables (POVMs) and analyze the relation
between the notions of non-disturbance, joint measurability and commutativity.
We specify conditions under which these properties coincide or
differ---depending for instance on the interplay between the number of outcomes
and the Hilbert space dimension or on algebraic properties of the effect
operators. We also show that (non-)disturbance is in general not a symmetric
relation and that it can be decided and quantified by means of a semidefinite
program.
