Errors in quantum tomography: diagnosing systematic versus statistical errors
A prime goal of quantum tomography is to provide quantitatively rigorous characterization of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in quantum information science. A range of techniques exist to enabl...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2013-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/15/3/035003 |
| _version_ | 1797751635517112320 |
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| author | Nathan K Langford |
| author_facet | Nathan K Langford |
| author_sort | Nathan K Langford |
| collection | DOAJ |
| description | A prime goal of quantum tomography is to provide quantitatively rigorous characterization of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in quantum information science. A range of techniques exist to enable the calculation of errors, such as Monte-Carlo simulations, but their quantitative value is arguably fundamentally flawed without an equally rigorous way of authenticating the quality of a reconstruction to ensure it provides a reasonable representation of the data, given the known noise sources. A key motivation for developing such a tool is to enable experimentalists to rigorously diagnose the presence of technical noise in their tomographic data. In this work, I explore the performance of the chi-squared goodness-of-fit test statistic as a measure of reconstruction quality. I show that its behaviour deviates noticeably from expectations for states lying near the boundaries of physical state space, severely undermining its usefulness as a quantitative tool precisely in the region which is of most interest in quantum information processing tasks. I suggest a simple, heuristic approach to compensate for these effects and present numerical simulations showing that this approach provides substantially improved performance. |
| first_indexed | 2024-03-12T16:51:25Z |
| format | Article |
| id | doaj.art-36436f3841d145c289e6f9b2d6cd22a2 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:51:25Z |
| publishDate | 2013-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-36436f3841d145c289e6f9b2d6cd22a22023-08-08T11:08:27ZengIOP PublishingNew Journal of Physics1367-26302013-01-0115303500310.1088/1367-2630/15/3/035003Errors in quantum tomography: diagnosing systematic versus statistical errorsNathan K Langford0Department of Physics, Royal Holloway University of London , Egham, Surrey TW20 0EX, UKA prime goal of quantum tomography is to provide quantitatively rigorous characterization of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in quantum information science. A range of techniques exist to enable the calculation of errors, such as Monte-Carlo simulations, but their quantitative value is arguably fundamentally flawed without an equally rigorous way of authenticating the quality of a reconstruction to ensure it provides a reasonable representation of the data, given the known noise sources. A key motivation for developing such a tool is to enable experimentalists to rigorously diagnose the presence of technical noise in their tomographic data. In this work, I explore the performance of the chi-squared goodness-of-fit test statistic as a measure of reconstruction quality. I show that its behaviour deviates noticeably from expectations for states lying near the boundaries of physical state space, severely undermining its usefulness as a quantitative tool precisely in the region which is of most interest in quantum information processing tasks. I suggest a simple, heuristic approach to compensate for these effects and present numerical simulations showing that this approach provides substantially improved performance.https://doi.org/10.1088/1367-2630/15/3/035003 |
| spellingShingle | Nathan K Langford Errors in quantum tomography: diagnosing systematic versus statistical errors New Journal of Physics |
| title | Errors in quantum tomography: diagnosing systematic versus statistical errors |
| title_full | Errors in quantum tomography: diagnosing systematic versus statistical errors |
| title_fullStr | Errors in quantum tomography: diagnosing systematic versus statistical errors |
| title_full_unstemmed | Errors in quantum tomography: diagnosing systematic versus statistical errors |
| title_short | Errors in quantum tomography: diagnosing systematic versus statistical errors |
| title_sort | errors in quantum tomography diagnosing systematic versus statistical errors |
| url | https://doi.org/10.1088/1367-2630/15/3/035003 |
| work_keys_str_mv | AT nathanklangford errorsinquantumtomographydiagnosingsystematicversusstatisticalerrors |