  Incompatibility of quantum devices is a useful resource in various quantum
information theoretical tasks, and it is at the heart of some fundamental
features of quantum theory. While the incompatibility of measurements and
quantum channels is well-studied, the incompatibility of quantum instruments
has not been explored in much detail. In this work, we revise a notion of
instrument compatibility introduced in the literature that we call traditional
compatibility. Then, we introduce the new notion of parallel compatibility, and
show that these two notions are inequivalent. Then, we argue that the notion of
traditional compatibility is incomplete, and prove that while parallel
compatibility captures measurement and channel compatibility, traditional
compatibility does not. Hence, we propose parallel compatibility as the
conceptually complete definition of compatibility of quantum instruments.
