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Constructions of good entanglement-assisted quantum error correcting codes

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Abstract

Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared entanglement between the sender and receiver. However, in general it is not easy to determine the number of shared pairs required to construct an EAQECC. In this paper, we show that this number is related to the hull of the classical code. Using this fact, we give methods to construct EAQECCs requiring desirable amounts of entanglement. This allows for designing families of EAQECCs with good error performance. Moreover, we construct maximal entanglement EAQECCs from LCD codes. Finally, we prove the existence of asymptotically good EAQECCs in the odd characteristic case.

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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments and suggestions. S. Jitman is supported by the Thailand Research Fund under Research Grant TRG5780065.

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Authors and Affiliations

  1. Faculty of Mathematics USTHB, University of Science and Technology of Algiers, Bab Ezzouar, Algeria

    Kenza Guenda

  2. Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand

    Somphong Jitman

  3. Department of Electrical and Computer Engineering, University of Victoria, PO Box 1700, STN CSC, Victoria, BC, V8W 2Y2, Canada

    T. Aaron Gulliver

Authors
  1. Kenza Guenda
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  2. Somphong Jitman
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  3. T. Aaron Gulliver
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Correspondence to Somphong Jitman.

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Communicated by V. D. Tonchev.

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Guenda, K., Jitman, S. & Gulliver, T.A. Constructions of good entanglement-assisted quantum error correcting codes. Des. Codes Cryptogr. 86, 121–136 (2018). https://doi.org/10.1007/s10623-017-0330-z

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  • DOI: https://doi.org/10.1007/s10623-017-0330-z

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