Comparison of confidence regions for quantum state tomography
The quantum state associated to an unknown experimental preparation procedure can be determined by performing quantum state tomography. If the statistical uncertainty in the data dominates over other experimental errors, then a tomographic reconstruction procedure must express this uncertainty. A ri...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ad06d9 |
| _version_ | 1797629612567560192 |
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| author | Jessica O de Almeida Matthias Kleinmann Gael Sentís |
| author_facet | Jessica O de Almeida Matthias Kleinmann Gael Sentís |
| author_sort | Jessica O de Almeida |
| collection | DOAJ |
| description | The quantum state associated to an unknown experimental preparation procedure can be determined by performing quantum state tomography. If the statistical uncertainty in the data dominates over other experimental errors, then a tomographic reconstruction procedure must express this uncertainty. A rigorous way to accomplish this is via statistical confidence regions (CRs) in state space. Naturally, the size of this region decreases when increasing the number of samples, but it also depends critically on the construction method of the region. We compare recent methods for constructing CRs as well as a reference method based on a Gaussian approximation. For the comparison, we propose an operational measure with the finding, that there is a significant difference between methods, but which method is preferable can depend on the details of the state preparation scenario. |
| first_indexed | 2024-03-11T10:56:42Z |
| format | Article |
| id | doaj.art-de2d43ce7a2f475b95c6804b97c0fcd7 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-11T10:56:42Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-de2d43ce7a2f475b95c6804b97c0fcd72023-11-13T09:20:47ZengIOP PublishingNew Journal of Physics1367-26302023-01-01251111301810.1088/1367-2630/ad06d9Comparison of confidence regions for quantum state tomographyJessica O de Almeida0https://orcid.org/0000-0001-5001-0555Matthias Kleinmann1Gael Sentís2ICFO—Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology , 08860 Castelldefels (Barcelona), SpainNaturwissenschaftlich-Technische Fakultät , Universität Siegen,Walter-Flex-Straße 3, 57068 Siegen, GermanyFísica Teórica: Informació i Fenòmens Quántics , Departament de Fisica, Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), SpainThe quantum state associated to an unknown experimental preparation procedure can be determined by performing quantum state tomography. If the statistical uncertainty in the data dominates over other experimental errors, then a tomographic reconstruction procedure must express this uncertainty. A rigorous way to accomplish this is via statistical confidence regions (CRs) in state space. Naturally, the size of this region decreases when increasing the number of samples, but it also depends critically on the construction method of the region. We compare recent methods for constructing CRs as well as a reference method based on a Gaussian approximation. For the comparison, we propose an operational measure with the finding, that there is a significant difference between methods, but which method is preferable can depend on the details of the state preparation scenario.https://doi.org/10.1088/1367-2630/ad06d9confidence regionsquantum state tomographystatistical uncertaintyconfidence regions compative method |
| spellingShingle | Jessica O de Almeida Matthias Kleinmann Gael Sentís Comparison of confidence regions for quantum state tomography New Journal of Physics confidence regions quantum state tomography statistical uncertainty confidence regions compative method |
| title | Comparison of confidence regions for quantum state tomography |
| title_full | Comparison of confidence regions for quantum state tomography |
| title_fullStr | Comparison of confidence regions for quantum state tomography |
| title_full_unstemmed | Comparison of confidence regions for quantum state tomography |
| title_short | Comparison of confidence regions for quantum state tomography |
| title_sort | comparison of confidence regions for quantum state tomography |
| topic | confidence regions quantum state tomography statistical uncertainty confidence regions compative method |
| url | https://doi.org/10.1088/1367-2630/ad06d9 |
| work_keys_str_mv | AT jessicaodealmeida comparisonofconfidenceregionsforquantumstatetomography AT matthiaskleinmann comparisonofconfidenceregionsforquantumstatetomography AT gaelsentis comparisonofconfidenceregionsforquantumstatetomography |