Maximal-entanglement EA Galois-qudit stabilizer code

Maximal-entanglement EA Galois-qudit stabilizer code[1,2]

Description

An \([[n,k,d;e]]_q\) EA Galois-qudit stabilizer code for which \(e = n-k\).

Rate

Maximal entanglement is required to achieve the EA hashing bound for the depolarizing channel using the father protocol from Refs. [3,4]; see [1; Footnote 2].

Parent

EA Galois-qudit stabilizer code

Cousins

EA quantum turbo code — Maximal-entanglement EA quantum turbo codes come close to achieving the EA hashing bound [5]; see [1; Footnote 2].
EA quantum LCD code — Asymptotically good maximal-entanglement EA Galois-qudit stabilizer codes can be constructed from LCD codes [6].

References

[1]: C.-Y. Lai, T. A. Brun, and M. M. Wilde, “Duality in Entanglement-Assisted Quantum Error Correction”, IEEE Transactions on Information Theory 59, 4020 (2013) arXiv:1302.4150 DOI
[2]: J. Qian and L. Zhang, “Entanglement-assisted quantum codes from arbitrary binary linear codes”, Designs, Codes and Cryptography 77, 193 (2014) DOI
[3]: I. Devetak, A. W. Harrow, and A. Winter, “A Family of Quantum Protocols”, Physical Review Letters 93, (2004) arXiv:quant-ph/0308044 DOI
[4]: I. Devetak, A. W. Harrow, and A. J. Winter, “A Resource Framework for Quantum Shannon Theory”, IEEE Transactions on Information Theory 54, 4587 (2008) arXiv:quant-ph/0512015 DOI
[5]: M. M. Wilde, M.-H. Hsieh, and Z. Babar, “Entanglement-Assisted Quantum Turbo Codes”, IEEE Transactions on Information Theory 60, 1203 (2014) arXiv:1010.1256 DOI
[6]: K. Guenda, S. Jitman, and T. A. Gulliver, “Constructions of Good Entanglement-Assisted Quantum Error Correcting Codes”, (2016) arXiv:1606.00134

Page edit log

Victor V. Albert (2023-07-18) — most recent

Cite as:

“Maximal-entanglement EA Galois-qudit stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/maximal_entanglement_galois_stabilizer

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/ea_stabilizer/maximal_entanglement_galois_stabilizer.yml.