Lower Bounds on Pauli Manipulation Detection Codes

Keiya Ichikawa; Kenji Yasunaga

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arXiv · 2504.00357

Lower Bounds on Pauli Manipulation Detection Codes

Keiya Ichikawa·Kenji Yasunaga

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Abstract

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 $R \leq 1 - \frac{2}{n}\log_q\left(\frac{1}{\epsilon}\right) + o(1)$, where $\epsilon$ is the error parameter.

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Keiya Ichikawa, Kenji Yasunaga. 2025-04-01. Lower Bounds on Pauli Manipulation Detection Codes. https://arxiv.org/abs/2504.00357

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