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In the present work, we develop a general framework for characterizing the admissible levels of loss and noise in a wide range of scenarios and protocols with untrusted measurement devices. In particular, we present general bounds that apply to prepare-and-measure protocols for the semi-DI approach, as well as to Bell tests for DI protocols. A key step in our work is to establish a general connection between quantum protocols with untrusted measurement devices and the fundamental notions of channel extendibility and joint-measurability, which capture essential aspects of the communication and measurement of quantum information. In particular, this leads us to introduce the notion of partial joint-measurability, which naturally arises within quantum cryptography.<\/jats:p>","DOI":"10.22331\/q-2024-12-23-1574","type":"journal-article","created":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T13:08:17Z","timestamp":1734959297000},"page":"1574","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Joint-measurability and quantum communication with untrusted devices"],"prefix":"10.22331","volume":"8","author":[{"given":"Michele","family":"Masini","sequence":"first","affiliation":[{"name":"Laboratoire d&apos;Information Quantique, Universit\u00e9 libre de Bruxelles (ULB), Belgium"}]},{"given":"Marie","family":"Ioannou","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Geneva, Switzerland"}]},{"given":"Nicolas","family":"Brunner","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Geneva, Switzerland"}]},{"given":"Stefano","family":"Pironio","sequence":"additional","affiliation":[{"name":"Laboratoire d&apos;Information Quantique, Universit\u00e9 libre de Bruxelles (ULB), Belgium"}]},{"given":"Pavel","family":"Sekatski","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Geneva, Switzerland"}]}],"member":"9598","published-online":{"date-parts":[[2024,12,23]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. 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