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Entanglement-assisted concatenated quantum codes

Author(s): Fan, Jihao; Li, Jun; Zhou, Yongbin; Hsieh, Min-Hsiu; Poor, H Vincent

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Abstract: Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show significant advantages over standard concatenated quantum codes (CQCs). First, we prove that, unlike standard CQCs, EACQCs can beat the nondegenerate Hamming bound for entanglement-assisted quantum error-correction codes (EAQECCs). Second, we construct families of EACQCs with parameters better than the best-known standard quantum error-correction codes (QECCs) and EAQECCs. Moreover, these EACQCs require very few Einstein–Podolsky–Rosen (EPR) pairs to begin with. Finally, it is shown that EACQCs make entanglement-assisted quantum communication possible, even if the ebits are noisy. Furthermore, EACQCs can outperform CQCs in entanglement fidelity over depolarizing channels if the ebits are less noisy than the qubits. We show that the error-probability threshold of EACQCs is larger than that of CQCs when the error rate of ebits is sufficiently lower than that of qubits. Specifically, we derive a high threshold of 47% when the error probability of the preshared entanglement is 1% to that of qubits.
Publication Date: 10-Jun-2022
Citation: Fan, Jihao, Li, Jun, Zhou, Yongbin, Hsieh, Min-Hsiu, Poor, H Vincent. (2022). Entanglement-assisted concatenated quantum codes. Proceedings of the National Academy of Sciences, 119 (24), 10.1073/pnas.2202235119
DOI: doi:10.1073/pnas.2202235119
ISSN: 0027-8424
EISSN: 1091-6490
Language: en
Type of Material: Journal Article
Journal/Proceeding Title: Proceedings of the National Academy of Sciences
Version: Final published version. This is an open access article.

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