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We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the &#x03B1;<\/mml:mi><\/mml:math>-z<\/mml:mi><\/mml:math> R\u00e9nyi relative entropy of magic. This allows us to identify a continuous set of magic monotones that are additive for single-qubit states. We also show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise. Finally, we obtain closed-form expressions for several states and tighter lower bounds for the overhead of probabilistic one-shot magic state distillation.<\/jats:p>","DOI":"10.22331\/q-2024-10-04-1492","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T07:40:17Z","timestamp":1728027617000},"page":"1492","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7914-671X","authenticated-orcid":false,"given":"Roberto","family":"Rubboli","sequence":"first","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3837-8159","authenticated-orcid":false,"given":"Ryuji","family":"Takagi","sequence":"additional","affiliation":[{"name":"Department of Basic Science, The University of Tokyo, Tokyo 153-8902, Japan"},{"name":"Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5410-3329","authenticated-orcid":false,"given":"Marco","family":"Tomamichel","sequence":"additional","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore"},{"name":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore"}]}],"member":"9598","published-online":{"date-parts":[[2024,10,4]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Victor Veitch, SA Hamed Mousavian, Daniel Gottesman, and Joseph Emerson. ``The resource theory of stabilizer quantum computation''. 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