Robustness of asymmetry and coherence of quantum states
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.
- Official publication in Physical Review A
- Preprint from arXiv:1601.03782 [quant-ph]
- Local preprint [pdf]
- M. Piani, M. Cianciaruso, T. R. Bromley, C. Napoli, N. Johnston, and G. Adesso. Robustness of asymmetry and coherence of quantum states, Physical Review A, 93:042107, 2016.
- Robustness of coherence: An operational and observable measure of quantum coherence (shorter publication focusing just on the robustness of coherence)