Local certification of unitary operations
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910587795013632 |
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| author | Kukulski, Ryszard Stępniak, Mateusz Hendzel, Kamil Pawela, Łukasz Gardas, Bartłomiej Puchała, Zbigniew |
| author_facet | Kukulski, Ryszard Stępniak, Mateusz Hendzel, Kamil Pawela, Łukasz Gardas, Bartłomiej Puchała, Zbigniew |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17037 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local certification of unitary operations Kukulski, Ryszard Stępniak, Mateusz Hendzel, Kamil Pawela, Łukasz Gardas, Bartłomiej Puchała, Zbigniew Quantum Physics 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. |
| title | Local certification of unitary operations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.17037 |