Robustness of asymmetry and coherence of quantum states

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

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.

Citation

Piani, M., Cianciaruso, M., Bromley, T. R., Napoli, C., Johnston, N., & Adesso, G. (2016). Robustness of asymmetry and coherence of quantum states. Physical Review A, 93(4), Article 042107. https://doi.org/10.1103/PhysRevA.93.042107

• Journal Article Type: Article
• Acceptance Date: Mar 4, 2016
• Online Publication Date: Apr 12, 2016
• Publication Date: Apr 12, 2016
• Deposit Date: Feb 24, 2017
• Publicly Available Date: Feb 24, 2017
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 93
• Issue: 4
• Article Number: 042107
• DOI: https://doi.org/10.1103/PhysRevA.93.042107
• Public URL: https://nottingham-repository.worktribe.com/output/785617
• Publisher URL: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.042107
• Related Public URLs: https://arxiv.org/abs/1601.03782
• Contract Date: Feb 24, 2017