Universal freezing of asymmetry

TL;DR

This paper establishes a universal condition under which the asymmetry of quantum states remains completely unaffected by covariant noise, revealing a fundamental aspect of quantum resource preservation.

Contribution

It proves that all asymmetry measures are frozen if and only if the relative entropy of asymmetry is frozen, demonstrating a universal freezing condition.

Findings

All asymmetry measures are frozen under covariant operations if the relative entropy of asymmetry is frozen.

The paper provides a necessary and sufficient condition for the total preservation of quantum asymmetry.

Universal freezing of asymmetry is characterized by the invariance of the relative entropy of asymmetry.

Abstract

Asymmetry of quantum states is a useful resource in applications such as quantum metrology, quantum communication, and reference frame alignment. However, asymmetry of a state tends to be degraded in physical scenarios where environment-induced noise is described by covariant operations, e.g., open systems constrained by superselection rules, and such degradations weaken the abilities of the state to implement quantum information processing tasks. In this paper, we investigate under which dynamical conditions asymmetry of a state is totally unaffected by the noise described by covariant operations. We find that all asymmetry measures are frozen for a state under a covariant operation if and only if the relative entropy of asymmetry is frozen for the state. Our finding reveals the existence of universal freezing of asymmetry, and provides a necessary and sufficient condition under which asymmetry is totally unaffected by the noise.