Abstract
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators we present a complete classification of the incompatibility of a given measurement assemblage with members. Detailed examples are given to the incompatibility for unbiased qubit measurements based on semidefinite programm.
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