Maximal entanglement entanglement-assisted quantum codes constructed from linear codes

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• 作者：Liangdong Lu (1)
  Ruihu Li (1)
  Luobin Guo (1)
  Qiang Fu (1)
  
  1. School of Science ; Air Force Engineering University ; Xi鈥檃n ; 710051 ; Shaanxi ; People鈥檚 Republic of China
  
• 关键词：EAQECC ; Maximal entanglement ; EA ; quantum Plotkin bound ; Optimal code
• 刊名：Quantum Information Processing
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：14
• 期：1
• 页码：165-182
• 全文大小：217 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Mathematics
  Engineering, general
  Computer Science, general
  Characterization and Evaluation Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-1332

文摘

An entanglement-assisted quantum error-correcting code (EAQECC) is a generalization of standard stabilizer quantum code. Maximal entanglement EAQECCs can achieve the EA-hashing bound asymptotically. In this work, the construction of quaternary zero radical codes is discussed, including the construction of low- dimensional quaternary codes for all code lengths and higher- dimensional quaternary codes for short lengths. Using the obtained quaternary codes, we construct many maximal entanglement EAQECCs with very good parameters. Some of these EAQECCs are optimal codes, and some of them are better than previously known ones. Combining these results with known bounds, we formulate a table of upper and lower bounds on the minimum distance of any maximal entanglement EAQECCs with length up to 20 channel qubits.