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Our one-sided concentration inequalities for a quantum state require the N<\/mml:mi><\/mml:math>-qudit system to be permutation invariant and are thus de-Finetti type, but they are tighter than the one previously obtained. We show that the bound can further be tightened if each qudit system has an additional symmetry. Furthermore, our concentration inequality for the outcomes of independent and identical measurements on an N<\/mml:mi><\/mml:math>-qudit quantum system has no assumption on the adversarial quantum state and is much tighter than the conventional one obtained through Azuma's inequality. We numerically demonstrate the tightness of our bounds in simple quantum information processing tasks.<\/jats:p>","DOI":"10.22331\/q-2024-11-27-1540","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T11:36:16Z","timestamp":1732707376000},"page":"1540","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Tight concentration inequalities for quantum adversarial setups exploiting permutation symmetry"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4164-4307","authenticated-orcid":false,"given":"Takaya","family":"Matsuura","sequence":"first","affiliation":[{"name":"Centre for Quantum Computation & Communication Technology, School of Science, RMIT University, Melbourne VIC 3000, Australia"},{"name":"RIKEN Center for Quantum Computing (RQC), Hirosawa 2-1, Wako, Saitama 351-0198, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3245-5344","authenticated-orcid":false,"given":"Shinichiro","family":"Yamano","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0512-5446","authenticated-orcid":false,"given":"Yui","family":"Kuramochi","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0745-6791","authenticated-orcid":false,"given":"Toshihiko","family":"Sasaki","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"},{"name":"Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4518-1461","authenticated-orcid":false,"given":"Masato","family":"Koashi","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"},{"name":"Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"}]}],"member":"9598","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Wassily Hoeffding. ``Probability Inequalities for Sums of Bounded Random Variables''. 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