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Abstract
En 中文
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.
Keywords:
entanglement
non-commutativity
non-binary stabilizer codes
quantum error-correction
quantum circuits
bounds
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