{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T00:51:21Z","timestamp":1775263881819,"version":"3.50.1"},"reference-count":36,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T00:00:00Z","timestamp":1592784000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Coherent and anticoherent states of spin systems up to spin <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>j<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:math> are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>j<\/mml:mi><\/mml:math>. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>j<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>7<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>2<\/mml:mn><\/mml:math> and (ii) for small rotation angles in the case of spin quantum numbers up to <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>j<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>5<\/mml:mn><\/mml:math>. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>j<\/mml:mi><\/mml:math>.<\/jats:p>","DOI":"10.22331\/q-2020-06-22-285","type":"journal-article","created":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T16:01:51Z","timestamp":1592841711000},"page":"285","source":"Crossref","is-referenced-by-count":27,"title":["Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0804-959X","authenticated-orcid":false,"given":"John","family":"Martin","sequence":"first","affiliation":[{"name":"Institut de Physique Nucl\u00e9aire, Atomique et de Spectroscopie, CESAM, University of Li\u00e8ge, B-4000 Li\u00e8ge, Belgium"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6647-3252","authenticated-orcid":false,"given":"Stefan","family":"Weigert","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of York, UK-York YO10 5DD, United Kingdom"}]},{"given":"Olivier","family":"Giraud","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France"}]}],"member":"9598","published-online":{"date-parts":[[2020,6,22]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"W. 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