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Bounds on concatenated entanglement-assisted quantum error-correcting codes

Name: Bounds on concatenated entanglement-assisted quantum error-correcting codes
Keywords: Quantum Physics, FOS: Physical sciences, Quantum Physics (quant-ph)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Jan 2024Publisher:arXiv

Authors: Dash, Nihar Ranjan; Dutta, Sanjoy; Srikanth, R.; Banerjee, Subhashish;

doi: 10.48550/arxiv.2412.16082

arXiv: http://arxiv.org/abs/2412.16082

Bounds on concatenated entanglement-assisted quantum error-correcting codes

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Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-shared entanglement to enhance the rate of error correction and communication. We study the concatenation of EAQECCs, in specific showing how the order of concatenation affects the number of ebits consumed, the logical error probability, the pseudo-threshold, and the violation of the quantum Hamming bound. We find that if the quaternary code from which an EAQECC is derived saturates the Griesmer (resp., Plotkin) bound, then the derived code will saturate the Griesmer (resp., linear Plotkin) bound for EAQECCs. We present families of concatenated EAQECCs that saturate the quantum Singleton, Griesmer, and linear Plotkin bounds for EAQECCs.

9 pages, 6 figures

Keywords

Quantum Physics, FOS: Physical sciences, Quantum Physics (quant-ph)

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