TY - JOUR
T1 - Entanglement-assisted concatenated quantum codes
AU - Fan, Jihao
AU - Li, Jun
AU - Zhou, Yongbin
AU - Hsieh, Min Hsiu
AU - Vincent Poor, H.
N1 - Funding Information:
ACKNOWLEDGMENTS. J.F. and M.-H.H. thank Markus Grassl for helpful discussions. This study was supported by National Natural Science Foundation of China Grant 61802175 and NSF Grant CCF-1908308.
Publisher Copyright:
Copyright © 2022 the Author(s).
PY - 2022/6/14
Y1 - 2022/6/14
N2 - 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.
AB - 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.
KW - concatenated quantum code
KW - entanglement fidelity
KW - entanglement-assisted quantum error-correction code
KW - error-correction code
KW - quantum Hamming bound
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U2 - 10.1073/pnas.2202235119
DO - 10.1073/pnas.2202235119
M3 - Article
C2 - 35687669
AN - SCOPUS:85131903730
SN - 0027-8424
VL - 119
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 24
M1 - e2202235119
ER -