Smooth Metric Adjusted Skew Information Rates

TL;DR

This paper introduces smooth metric adjusted skew information rates, a new class of asymmetry measures in quantum resource theory, which are valid in the asymptotic limit and bound coherence costs and distillation.

Contribution

It proposes a novel smoothing technique for metric adjusted skew information, ensuring valid asymptotic rates in quantum asymmetry resource theory.

Findings

Provides lower bounds for coherence cost

Establishes upper bounds for distillable coherence

Ensures asymptotic validity of skew information measures

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.