Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
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| Format: | Preprint |
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2023
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| _version_ | 1866911244456296448 |
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| author | Drótos, Gábor Pál, Károly F. Vértesi, Tamás |
| author_facet | Drótos, Gábor Pál, Károly F. Vértesi, Tamás |
| contents | Self-testing is a powerful method for certifying quantum systems. Initially proposed in the device-independent (DI) setting, self-testing has since been relaxed to the semi-device-independent (semi-DI) setting. In this study, we focus on the self-testing of a specific type of non-projective qubit measurements belonging to a one-parameter family, using the semi-DI prepare-and-measure (PM) scenario. Remarkably, we identify the simplest PM scenario discovered so far, involving only four preparations and four measurements, for self-testing the fourth measurement. This particular measurement is a four-outcome non-projective positive operator-valued measure (POVM) and falls in the class of semisymmetric informationally complete (semi-SIC) POVMs introduced by Geng et al. [Phys. Rev. Lett. 126, 100401 (2021)]. To achieve this, we develop analytical techniques for semi-DI self-testing in the PM scenario. Our results shall pave the way towards self-testing any extremal qubit POVM within a potentially minimal PM scenario. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_07248 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario Drótos, Gábor Pál, Károly F. Vértesi, Tamás Quantum Physics Self-testing is a powerful method for certifying quantum systems. Initially proposed in the device-independent (DI) setting, self-testing has since been relaxed to the semi-device-independent (semi-DI) setting. In this study, we focus on the self-testing of a specific type of non-projective qubit measurements belonging to a one-parameter family, using the semi-DI prepare-and-measure (PM) scenario. Remarkably, we identify the simplest PM scenario discovered so far, involving only four preparations and four measurements, for self-testing the fourth measurement. This particular measurement is a four-outcome non-projective positive operator-valued measure (POVM) and falls in the class of semisymmetric informationally complete (semi-SIC) POVMs introduced by Geng et al. [Phys. Rev. Lett. 126, 100401 (2021)]. To achieve this, we develop analytical techniques for semi-DI self-testing in the PM scenario. Our results shall pave the way towards self-testing any extremal qubit POVM within a potentially minimal PM scenario. |
| title | Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2306.07248 |