Local certification of unitary operations
Abstract In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-75148-z |
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| _version_ | 1846171951031123968 |
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| author | Ryszard Kukulski Mateusz Stępniak Kamil Hendzel Łukasz Pawela Bartłomiej Gardas Zbigniew Puchała |
| author_facet | Ryszard Kukulski Mateusz Stępniak Kamil Hendzel Łukasz Pawela Bartłomiej Gardas Zbigniew Puchała |
| author_sort | Ryszard Kukulski |
| collection | DOAJ |
| description | Abstract In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement with auxiliary systems. Our result indicates connection of the local certification problem with a product numerical range of unitary matrices. We show that the optimal local strategy does not need usage of auxiliary systems and requires only single round of one-way classical communication. Moreover, we compare local and global certification strategies and show that typically local strategies are optimal, yet in some extremal cases, where global strategies make no errors, local ones may fail miserably. Finally, some application for local certification of von Neumann measurements are discussed as well. |
| format | Article |
| id | doaj-art-4a19bf4b3dfb46509e517c06b42c70de |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-4a19bf4b3dfb46509e517c06b42c70de2024-11-10T12:23:04ZengNature PortfolioScientific Reports2045-23222024-11-011411810.1038/s41598-024-75148-zLocal certification of unitary operationsRyszard Kukulski0Mateusz Stępniak1Kamil Hendzel2Łukasz Pawela3Bartłomiej Gardas4Zbigniew Puchała5Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian UniversityQuantumz.io Sp. z o.o.Quantumz.io Sp. z o.o.Institute of Theoretical and Applied Informatics, Polish Academy of SciencesInstitute of Theoretical and Applied Informatics, Polish Academy of SciencesInstitute of Theoretical and Applied Informatics, Polish Academy of SciencesAbstract In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement with auxiliary systems. Our result indicates connection of the local certification problem with a product numerical range of unitary matrices. We show that the optimal local strategy does not need usage of auxiliary systems and requires only single round of one-way classical communication. Moreover, we compare local and global certification strategies and show that typically local strategies are optimal, yet in some extremal cases, where global strategies make no errors, local ones may fail miserably. Finally, some application for local certification of von Neumann measurements are discussed as well.https://doi.org/10.1038/s41598-024-75148-z |
| spellingShingle | Ryszard Kukulski Mateusz Stępniak Kamil Hendzel Łukasz Pawela Bartłomiej Gardas Zbigniew Puchała Local certification of unitary operations Scientific Reports |
| title | Local certification of unitary operations |
| title_full | Local certification of unitary operations |
| title_fullStr | Local certification of unitary operations |
| title_full_unstemmed | Local certification of unitary operations |
| title_short | Local certification of unitary operations |
| title_sort | local certification of unitary operations |
| url | https://doi.org/10.1038/s41598-024-75148-z |
| work_keys_str_mv | AT ryszardkukulski localcertificationofunitaryoperations AT mateuszstepniak localcertificationofunitaryoperations AT kamilhendzel localcertificationofunitaryoperations AT łukaszpawela localcertificationofunitaryoperations AT bartłomiejgardas localcertificationofunitaryoperations AT zbigniewpuchała localcertificationofunitaryoperations |