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SCIENCE CHINA Information Sciences, Volume 60, Issue 4: 042501(2017) https://doi.org/10.1007/s11432-015-0932-y

Non-binary entanglement-assisted quantum stabilizer codes

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  • ReceivedMar 14, 2016
  • AcceptedApr 29, 2016
  • PublishedSep 13, 2016

Abstract

In this paper, we present the $p^m$-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.


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