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 rob...
| Main Authors: | , , , , , |
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| Format: | Article |
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American Physical Society
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40792/ |
| _version_ | 1848796134363889664 |
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| author | Piani, Marco Cianciaruso, Marco Bromley, Thomas R. Napoli, Carmine Johnston, Nathaniel Adesso, Gerardo |
| author_facet | Piani, Marco Cianciaruso, Marco Bromley, Thomas R. Napoli, Carmine Johnston, Nathaniel Adesso, Gerardo |
| author_sort | Piani, Marco |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:43:09Z |
| format | Article |
| id | nottingham-40792 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:09Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-407922020-05-04T17:47:01Z https://eprints.nottingham.ac.uk/40792/ Robustness of asymmetry and coherence of quantum states Piani, Marco Cianciaruso, Marco Bromley, Thomas R. Napoli, Carmine Johnston, Nathaniel Adesso, Gerardo 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. American Physical Society 2016-04-12 Article PeerReviewed Piani, Marco, Cianciaruso, Marco, Bromley, Thomas R., Napoli, Carmine, 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 http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.042107 doi:10.1103/PhysRevA.93.042107 doi:10.1103/PhysRevA.93.042107 |
| spellingShingle | Piani, Marco Cianciaruso, Marco Bromley, Thomas R. Napoli, Carmine Johnston, Nathaniel Adesso, Gerardo Robustness of asymmetry and coherence of quantum states |
| title | Robustness of asymmetry and coherence of quantum states |
| title_full | Robustness of asymmetry and coherence of quantum states |
| title_fullStr | Robustness of asymmetry and coherence of quantum states |
| title_full_unstemmed | Robustness of asymmetry and coherence of quantum states |
| title_short | Robustness of asymmetry and coherence of quantum states |
| title_sort | robustness of asymmetry and coherence of quantum states |
| url | https://eprints.nottingham.ac.uk/40792/ https://eprints.nottingham.ac.uk/40792/ https://eprints.nottingham.ac.uk/40792/ |