Robustness of asymmetry and coherence of quantum states

Marco Piani, Marco Cianciaruso, Thomas R. Bromley, Carmine Napoli, Nathaniel Johnston, Gerardo Adesso

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134 Citations (Scopus)
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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.
Original languageEnglish
Article number042107
Number of pages13
JournalPhysical Review A
Issue number4
Publication statusPublished - 12 Apr 2016


  • quantum states
  • asymmetry of states
  • quantum information processing

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