{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:42:34Z","timestamp":1760236954245,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,30]],"date-time":"2020-01-30T00:00:00Z","timestamp":1580342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 n members. Detailed examples are given for the incompatibility of unbiased qubit measurements based on a semidefinite program.<\/jats:p>","DOI":"10.3390\/e22020161","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T05:55:46Z","timestamp":1580450146000},"page":"161","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Note on the Hierarchy of Quantum Measurement Incompatibilities"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4514-1790","authenticated-orcid":false,"given":"Bao-Zhi","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China"}]},{"given":"Zhi-Xi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"}]},{"given":"Xianqing","family":"Li-Jost","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2412-8626","authenticated-orcid":false,"given":"Shao-Ming","family":"Fei","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"},{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1007\/BF01397280","article-title":"\u00dcber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik","volume":"43","author":"Heisenberg","year":"1927","journal-title":"Z. 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