Smooth Metric Adjusted Skew Information Rates

Koji Yamaguchi1 and Hiroyasu Tajima2,3

1Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
2Department of Communication Engineering and Informatics, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan
3JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan

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Abstract

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.

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Cited by

[1] Koji Yamaguchi and Hiroyasu Tajima, "Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information", Physical Review Letters 131 20, 200203 (2023).

[2] Daigo Kudo and Hiroyasu Tajima, "Fisher information matrix as a resource measure in the resource theory of asymmetry with general connected-Lie-group symmetry", Physical Review A 107 6, 062418 (2023).

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