Nondisturbing quantum measurements

We consider pairs of discrete quantum observables (POVMs) and analyze the relation between the notions of nondisturbance, 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. (C) 2010 American Institute of Physics. [doi:10.1063/1.3480658]