Compatibility of quantum instruments

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