Lower Bounds on Pauli Manipulation Detection Codes
arXiv:2504.003573.7h-index: 8
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Provides a fundamental lower bound for quantum error detection codes, relevant to quantum information theory.
The paper establishes the first trade-off between error parameter and coding rate for Pauli Manipulation Detection codes, showing that the rate is bounded by 1 - (2/n) log_q(1/ε) + o(1).
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.