Non-binary entanglement-assisted quantum stabilizer codes

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.