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However, its asymptotic rates are not valid asymmetry monotone since it has an asymptotic discontinuity. We here introduce a new class of asymmetry measures with the smoothing technique, which we term smooth metric adjusted skew information. We prove that its asymptotic sup- and inf-rates are valid asymptotic measures in the resource theory of asymmetry. Furthermore, it is proven that the smooth metric adjusted skew information rates provide a lower bound for the coherence cost and an upper bound for the distillable coherence.<\/jats:p>","DOI":"10.22331\/q-2023-05-22-1012","type":"journal-article","created":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T09:45:36Z","timestamp":1684748736000},"page":"1012","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":7,"title":["Smooth Metric Adjusted Skew Information Rates"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9723-6145","authenticated-orcid":false,"given":"Koji","family":"Yamaguchi","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hiroyasu","family":"Tajima","sequence":"additional","affiliation":[{"name":"Department of Communication Engineering and Informatics, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan"},{"name":"JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"E. 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