The i.i.d. State Convertibility in the Resource Theory of Asymmetry for Finite Groups

Abstract

We identify exact and approximate conversion rates between i.i.d. pure states under covariant operations in the resource theory of asymmetry for symmetries described by finite groups. We establish the formula for the exact conversion rate by completely specifying the relevant set of resource measures. The exact conversion is generally asymptotically irreversible due to the existence of multiple independent resource measures, and we find the necessary and sufficient condition for asymptotic reversibility. On the other hand, we show that the approximate conversion rates diverge or vanish, which implies that the asymmetry can be infinitely amplified if we allow a vanishingly small error. We reveal the underlying mechanism of such a counterintuitive phenomenon by utilizing the properties of maximally asymmetric states.