Optimizing nontrivial quantum observables using coherence
In this paper we consider the quantum resources required to maximize the mean values of any nontrivial quantum observable. We show that the task of maximizing the mean value of an observable is equivalent to maximizing some form of coherence, up to the application of an incoherent operation. For any...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab0430 |
| _version_ | 1827872886285664256 |
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| author | Kok Chuan Tan Seongjeon Choi Hyunseok Jeong |
| author_facet | Kok Chuan Tan Seongjeon Choi Hyunseok Jeong |
| author_sort | Kok Chuan Tan |
| collection | DOAJ |
| description | In this paper we consider the quantum resources required to maximize the mean values of any nontrivial quantum observable. We show that the task of maximizing the mean value of an observable is equivalent to maximizing some form of coherence, up to the application of an incoherent operation. For any nontrivial observable, there always exists a set of preferred basis states where the superposition between such states is always useful for optimizing the mean value of a quantum observable. The usefulness of such states is expressed in terms of an infinitely large family of valid coherence measures which is then shown to be efficiently computable via a semidefinite program. We also show that these coherence measures respect a hierarchy that gives the robustness of coherence and the l _1 norm of coherence additional operational significance in terms of such optimization tasks. |
| first_indexed | 2024-03-12T16:29:55Z |
| format | Article |
| id | doaj.art-e4e8a8a11bcb4980946810bb90f8290f |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:29:55Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-e4e8a8a11bcb4980946810bb90f8290f2023-08-08T15:33:45ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121202301310.1088/1367-2630/ab0430Optimizing nontrivial quantum observables using coherenceKok Chuan Tan0https://orcid.org/0000-0002-4025-1520Seongjeon Choi1Hyunseok Jeong2Center for Macroscopic Quantum Control & Institute of Applied Physics, Department of Physics and Astronomy, Seoul National University , Seoul, 08826, Republic of KoreaCenter for Macroscopic Quantum Control & Institute of Applied Physics, Department of Physics and Astronomy, Seoul National University , Seoul, 08826, Republic of KoreaCenter for Macroscopic Quantum Control & Institute of Applied Physics, Department of Physics and Astronomy, Seoul National University , Seoul, 08826, Republic of KoreaIn this paper we consider the quantum resources required to maximize the mean values of any nontrivial quantum observable. We show that the task of maximizing the mean value of an observable is equivalent to maximizing some form of coherence, up to the application of an incoherent operation. For any nontrivial observable, there always exists a set of preferred basis states where the superposition between such states is always useful for optimizing the mean value of a quantum observable. The usefulness of such states is expressed in terms of an infinitely large family of valid coherence measures which is then shown to be efficiently computable via a semidefinite program. We also show that these coherence measures respect a hierarchy that gives the robustness of coherence and the l _1 norm of coherence additional operational significance in terms of such optimization tasks.https://doi.org/10.1088/1367-2630/ab0430quantum coherencequantum resource theoriesquantum information |
| spellingShingle | Kok Chuan Tan Seongjeon Choi Hyunseok Jeong Optimizing nontrivial quantum observables using coherence New Journal of Physics quantum coherence quantum resource theories quantum information |
| title | Optimizing nontrivial quantum observables using coherence |
| title_full | Optimizing nontrivial quantum observables using coherence |
| title_fullStr | Optimizing nontrivial quantum observables using coherence |
| title_full_unstemmed | Optimizing nontrivial quantum observables using coherence |
| title_short | Optimizing nontrivial quantum observables using coherence |
| title_sort | optimizing nontrivial quantum observables using coherence |
| topic | quantum coherence quantum resource theories quantum information |
| url | https://doi.org/10.1088/1367-2630/ab0430 |
| work_keys_str_mv | AT kokchuantan optimizingnontrivialquantumobservablesusingcoherence AT seongjeonchoi optimizingnontrivialquantumobservablesusingcoherence AT hyunseokjeong optimizingnontrivialquantumobservablesusingcoherence |