泡利操纵检测码的下界

IF 2.6 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2026-07-01 Epub Date: 2026-04-22 DOI:10.1109/TIT.2026.3686419

Keiya Ichikawa;Kenji Yasunaga

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引用次数: 0

摘要

我们给出了泡利操作检测码（PMD）的下界，这是一类高概率检测每个泡利错误的量子码。我们的下界揭示了错误参数和编码率之间的第一个权衡。具体来说，我们证明了每个$q$ -任意长度为$n$和编码率为$R$的PMD码必须满足$R \leq 1 - \frac {2}{n}\log _{q}\left ({ \frac {1}{\varepsilon }}\right) + o(1)$，其中$\varepsilon $为误差参数。

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Lower Bounds on Pauli Manipulation Detection Codes

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

$R \leq 1 - \frac {2}{n}\log _{q}\left ({ \frac {1}{\varepsilon }}\right) + o(1)$

, where

$\varepsilon $

is the error parameter.

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来源期刊

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.