Quantum $X$-Secure $B$-Byzantine $T$-Colluding Private Information Retrieval
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911869887840256 |
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| author | Nomeir, Mohamed Aytekin, Alptug Ulukus, Sennur |
| author_facet | Nomeir, Mohamed Aytekin, Alptug Ulukus, Sennur |
| contents | We consider the problems arising from the presence of Byzantine servers in a quantum private information retrieval (QPIR) setting. This is the first work to precisely define what the capabilities of Byzantine servers could be in a QPIR context. We show that quantum Byzantine servers have more capabilities than their classical counterparts due to the possibilities created by quantum encoding procedures. We focus on quantum Byzantine servers that can apply any reversible operation on their individual qudits. In this case, Byzantine servers can generate any error, i.e., this covers \emph{all} possible single qudit operations that can be applied by Byzantine servers on their qudits. We design a scheme based on cross-subspace alignment (CSA) and we show that this scheme achieves superdense coding gain in some cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum $X$-Secure $B$-Byzantine $T$-Colluding Private Information Retrieval Nomeir, Mohamed Aytekin, Alptug Ulukus, Sennur Information Theory Cryptography and Security Networking and Internet Architecture Signal Processing Quantum Physics We consider the problems arising from the presence of Byzantine servers in a quantum private information retrieval (QPIR) setting. This is the first work to precisely define what the capabilities of Byzantine servers could be in a QPIR context. We show that quantum Byzantine servers have more capabilities than their classical counterparts due to the possibilities created by quantum encoding procedures. We focus on quantum Byzantine servers that can apply any reversible operation on their individual qudits. In this case, Byzantine servers can generate any error, i.e., this covers \emph{all} possible single qudit operations that can be applied by Byzantine servers on their qudits. We design a scheme based on cross-subspace alignment (CSA) and we show that this scheme achieves superdense coding gain in some cases. |
| title | Quantum $X$-Secure $B$-Byzantine $T$-Colluding Private Information Retrieval |
| topic | Information Theory Cryptography and Security Networking and Internet Architecture Signal Processing Quantum Physics |
| url | https://arxiv.org/abs/2401.17252 |