Robustness of asymmetry and coherence of quantum states

TL;DR

This paper introduces and analyzes the robustness of asymmetry as a quantifier of quantum state asymmetry, providing computational methods, operational interpretations, and applications to coherence and quantum metrology.

Contribution

It defines the robustness of asymmetry, proves its properties, and connects it with practical measurement tools like witnesses and coherence, advancing understanding of quantum resources.

Findings

Robustness of asymmetry is efficiently computable via semidefinite programming.

Asymmetry witnesses can lower bound the robustness of asymmetry.

Robustness of coherence is analytically calculated for certain states and linked to phase discrimination.

Abstract

Quantum states may exhibit asymmetry with respect to the action of a given group. Such an asymmetry of states can be considered as a resource in applications such as quantum metrology, and it is a concept that encompasses quantum coherence as a special case. We introduce explicitly and study the robustness of asymmetry, a quantifier of asymmetry of states that we prove to have many attractive properties, including efficient numerical computability via semidefinite programming, and an operational interpretation in a channel discrimination context. We also introduce the notion of asymmetry witnesses, whose measurement in a laboratory detects the presence of asymmetry. We prove that properly constrained asymmetry witnesses provide lower bounds to the robustness of asymmetry, which is shown to be a directly measurable quantity itself. We then focus our attention on coherence witnesses and the robustness of coherence, for which we prove a number of additional results; these include an analysis of its specific relevance in phase discrimination and quantum metrology, an analytical calculation of its value for a relevant class of quantum states, and tight bounds that relate it to another previously defined coherence monotone.