Smooth Metric Adjusted Skew Information Rates

Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. However, its asymptotic rates are not valid asymmetry monotone since it has an asymptotic discontinuity. We here introduce a new class of asymme...

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Bibliographic Details
Published inQuantum (Vienna, Austria) Vol. 7; p. 1012
Main Authors Yamaguchi, Koji, Tajima, Hiroyasu
Format Journal Article
LanguageEnglish
Published Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 22.05.2023
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Summary:Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. 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.
ISSN:2521-327X
2521-327X
DOI:10.22331/q-2023-05-22-1012