Entanglement-Assisted Quantum Error Correcting Codes Over Nice Rings
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© 2014 IEEE. Entanglement-assisted quantum error correcting codes have the nice feature that they can be constructed from classical additive codes that do not need to be self-orthogonal- A n advantage over stabilizer codes. In the literature, these codes were investigated for finite fields, mostly binary fields. A generalization of the Pauli basis to nice error bases indexed by rings allows one to consider alphabet sizes that are not restricted to powers of a prime. The main goal of this paper is to show how entanglement-assisted quantum error correcting codes over nice rings can be constructed. We develop the rudiments of symplectic geometry over rings and prove that an R-module with antisymmetric bicharacter can be decomposed as an orthogonal direct sum of hyperbolic pairs.
author list (cited authors)
Lee, S., & Klappenecker, A.