Robustness of asymmetry and coherence of quantum states

Piani, Marco and Cianciaruso, Marco and Bromley, Thomas R. and Napoli, Carmine and Johnston, Nathaniel and Adesso, Gerardo (2016) Robustness of asymmetry and coherence of quantum states. Physical Review A, 93 . 042107/1-042107/13. ISSN 2469-9934

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1103/PhysRevA.93.042107
Related URLs:
Depositing User: Adesso, Gerardo
Date Deposited: 24 Feb 2017 09:16
Last Modified: 18 Oct 2017 18:54
URI: http://eprints.nottingham.ac.uk/id/eprint/40792

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