Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929409650327552 |
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| author | Diviánszky, Péter Márton, István Bene, Erika Vértesi, Tamás |
| author_facet | Diviánszky, Péter Márton, István Bene, Erika Vértesi, Tamás |
| contents | We address the problem of testing the quantumness of two-dimensional systems in the prepare-and-measure (PM) scenario, using a large number of preparations and a large number of measurement settings, with binary outcome measurements. In this scenario, we introduce constants, which we relate to the Grothendieck constant of order 3. We associate them with the white noise resistance of the prepared qubits and to the critical detection efficiency of the measurements performed. Large-scale numerical tools are used to bound the constants. This allows us to obtain new bounds on the minimum detection efficiency that a setup with 70 preparations and 70 measurement settings can tolerate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17185 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant Diviánszky, Péter Márton, István Bene, Erika Vértesi, Tamás Quantum Physics We address the problem of testing the quantumness of two-dimensional systems in the prepare-and-measure (PM) scenario, using a large number of preparations and a large number of measurement settings, with binary outcome measurements. In this scenario, we introduce constants, which we relate to the Grothendieck constant of order 3. We associate them with the white noise resistance of the prepared qubits and to the critical detection efficiency of the measurements performed. Large-scale numerical tools are used to bound the constants. This allows us to obtain new bounds on the minimum detection efficiency that a setup with 70 preparations and 70 measurement settings can tolerate. |
| title | Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2211.17185 |