EA MDS code

EA MDS code[1–3]

EA Galois-qudit code whose parameters make the EAQECC Singleton bound (a.k.a. qubit-ebit Singleton bound) [3; Thm. 6] become an equality.

The original EAQECC Singleton bound [1,4] was shown to be erroneous [5] and corrected in Ref. [3].

Quantum maximum-distance-separable (MDS) code
Maximum distance separable (MDS) code— MDS codes give rise to families of EA Galois-qudit codes that saturate the original (erroneous) EAQECC Singleton bound [6].
EA qubit stabilizer code— There exist concatenated EA qubit stabilizer codes that saturate the EA quantum Singleton bound [7].

Parents

EA MDS code

[1]: T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting Quantum Errors with Entanglement”, Science 314, 436 (2006) arXiv:quant-ph/0610092 DOI
[2]: C.-Y. Lai and T. A. Brun, “Entanglement increases the error-correcting ability of quantum error-correcting codes”, Physical Review A 88, (2013) arXiv:1008.2598 DOI
[3]: M. Grassl, F. Huber, and A. Winter, “Entropic Proofs of Singleton Bounds for Quantum Error-Correcting Codes”, IEEE Transactions on Information Theory 68, 3942 (2022) arXiv:2010.07902 DOI
[4]: T. A. Brun, I. Devetak, and M.-H. Hsieh, “Catalytic Quantum Error Correction”, IEEE Transactions on Information Theory 60, 3073 (2014) arXiv:quant-ph/0608027 DOI
[5]: M. Grassl, “Entanglement-assisted quantum communication beating the quantum Singleton bound”, Physical Review A 103, (2021) arXiv:2007.01249 DOI
[6]: J. Fan, H. Chen, and J. Xu, “Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1”, (2016) arXiv:1602.02235
[7]: N. R. Dash, S. Dutta, R. Srikanth, and S. Banerjee, “Bounds on concatenated entanglement-assisted quantum error-correcting codes”, (2024) arXiv:2412.16082

Page edit log

“EA MDS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ea_mds