Lower Bounds on Pauli Manipulation Detection Codes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908976713564160 |
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| author | Ichikawa, Keiya Yasunaga, Kenji |
| author_facet | Ichikawa, Keiya Yasunaga, Kenji |
| contents | We present a lower bound for Pauli Manipulation Detection (PMD) codes, a class of quantum codes that detect every Pauli error with high probability. Our lower bound reveals the first trade-off between the error parameter and the coding rate. Specifically, we show that every $q$-ary PMD code of length $n$ and coding rate $R$ must satisfy $R \leq 1 - \frac{2}{n}\log_q\left(\frac{1}ε\right) + o(1)$, where $ε$ is the error parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower Bounds on Pauli Manipulation Detection Codes Ichikawa, Keiya Yasunaga, Kenji Quantum Physics Cryptography and Security Information Theory We present a lower bound for Pauli Manipulation Detection (PMD) codes, a class of quantum codes that detect every Pauli error with high probability. Our lower bound reveals the first trade-off between the error parameter and the coding rate. Specifically, we show that every $q$-ary PMD code of length $n$ and coding rate $R$ must satisfy $R \leq 1 - \frac{2}{n}\log_q\left(\frac{1}ε\right) + o(1)$, where $ε$ is the error parameter. |
| title | Lower Bounds on Pauli Manipulation Detection Codes |
| topic | Quantum Physics Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2504.00357 |