Abstract
It is possible to construct an entanglement-assisted quantum error-correcting (EAQEC, for short) code from any classical linear code. However, the parameter of ebits \(c\) is usually calculated by computer search. In this work, we can construct a family of \([[2n-k, k, \ge d; c]]\) EAQEC codes from arbitrary binary \([n, k, d]\) linear codes, where the parameter of ebits \(c=2n-2k\) can be easily generated algebraically and not by computational search. Moreover, the constructed EAQEC codes are maximal-entanglement EAQEC codes. We also present a different method of constructing entanglement-assisted accumulator codes. Finally, we prove that asymptotically good EAQEC codes exist.
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Acknowledgments
We are indebted to the anonymous referees for their valuable comments and suggestions that helped to improve significantly the quality of this paper. This work was supported by the National Science Foundation of China (11126029, 11247001, 61170059, 61170172, 61272153 and 61340003); the Anhui Provincial Natural Science Foundation (1408085MA05).
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Communicated by J. Bierbrauer.
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Qian, J., Zhang, L. Entanglement-assisted quantum codes from arbitrary binary linear codes. Des. Codes Cryptogr. 77, 193–202 (2015). https://doi.org/10.1007/s10623-014-9997-6
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DOI: https://doi.org/10.1007/s10623-014-9997-6
Keywords
- Entanglement-assisted quantum error-correcting code
- Quantum error-correcting code
- Linear code
- Parity-check matrix