Non-binary entanglement-assisted quantum stabilizer codes

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• 作者：Lan Luo ; Zhi Ma ; Zhengchao Wei ; Riguang Leng
• 关键词：entanglement ; non ; commutativity ; non ; binary stabilizer codes ; quantum error ; correction ; quantum circuits ; bounds
• 刊名：SCIENCE CHINA Information Sciences
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：60
• 期：4
• 全文大小：425 KB
• 刊物类别：Computer Science
• 刊物主题：Chinese Library of Science
  Information Systems and Communication Service
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1919
• 卷排序：60

文摘

In this paper, we present the pm-ary entanglement-assisted (EA) stabilizer formalism, where p is a prime and m is a positive integer. Given an arbitrary non-abelian “stabilizer”, the problem of code construction and encoding is settled perfectly in the case of m = 1. The optimal number of required maximally entangled pairs is discussed and an algorithm to determine the encoding and decoding circuits is proposed. We also generalize several bounds on p-ary EA stabilizer codes, such as the BCH bound, the G-V bound and the linear programming bound. However, the issue becomes tricky when it comes to m > 1, in which case, the former construction method applies only when the non-commuting “stabilizer” satisfies a sophisticated limitation.