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Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system, generalizes incompatibility of channels and incompatibility of positive operator-valued measures (POVMs). We derive implications of instrument compatibility for the induced POVMs and channels. We also study relation of instrument compatibility to the concept of non-disturbance. Finally, we prove equivalence between instrument compatibility and postprocessing of certain instruments, which we term complementary instruments. We illustrate our findings on examples of various classes of instruments.<\/jats:p>","DOI":"10.22331\/q-2024-02-12-1246","type":"journal-article","created":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T13:54:11Z","timestamp":1707746051000},"page":"1246","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Incompatibility of quantum instruments"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9528-1583","authenticated-orcid":false,"given":"Leevi","family":"Lepp\u00e4j\u00e4rvi","sequence":"first","affiliation":[{"name":"RCQI, Institute of Physics, Slovak Academy of Sciences, D\u00fabravsk\u00e1 cesta 9, 84511 Bratislava, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9342-5862","authenticated-orcid":false,"given":"Michal","family":"Sedl\u00e1k","sequence":"additional","affiliation":[{"name":"RCQI, Institute of Physics, Slovak Academy of Sciences, D\u00fabravsk\u00e1 cesta 9, 84511 Bratislava, Slovakia"},{"name":"Faculty of Informatics, Masaryk University, Botanick\u00e1 68a, 602 00 Brno, Czech Republic"}]}],"member":"9598","published-online":{"date-parts":[[2024,2,12]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"W. 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