General quantum error-correcting code with entanglement based on codeword stabilized quantum code
Abstract
In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes, including additive and nonadditive codes, based on the codeword stabilized framework on subsystems. The codeword stabilized (CWS) framework is a scheme to construct quantum error-correcting codes (QECCs) including both additive and nonadditive codes, and gives a method to construct a QECC from a classical error-correcting code in standard form. Entangled pairs of qubits (ebits) can be used to improve capacity of quantum error correction. In addition, it gives a method to overcome the dual-containing constraint. Operator quantum error correction (OQEC) gives a general framework to construct quantum error-correcting codes. We construct OQEC codes with ebits based on the CWS framework. This new scheme, entanglement-assisted operator codeword stabilized (EAOCWS) quantum codes, is the most general framework we know of to construct both additive and nonadditive codes from classical error-correcting codes. We describe the formalism of our scheme, demonstrate the construction with examples, and give several EAOCWS codes.
Keywords
Cite
@article{arxiv.1311.1533,
title = {General quantum error-correcting code with entanglement based on codeword stabilized quantum code},
author = {Jeonghwan Shin and Jun Heo and Todd A. Brun},
journal= {arXiv preprint arXiv:1311.1533},
year = {2013}
}
Comments
8 pages, no figures, submitted to Physical Review A