2016/01/31 by Marco Piani, Marco Cianciaruso, Thomas R. Bromley +3 · 2 citations
Physics and Astronomy · Mathematics · #quant-ph #cond-mat.other #math-ph #math.MP #physics.comp-ph
paper · pdf · doi:10.1103/physreva.93.042107
published as Phys. Rev. A 93, 042107 (2016) · 14 pages, 1 figure. Close to published version. Matlab code included in the source. See also the companion letter arXiv:1601.03781
arxiv created 2016/04/12 · arxiv updated 2016/04/20
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.