Entanglement-assisted concatenated quantum codes

Jihao Fan, Jun Li, Yongbin Zhou, Min Hsiu Hsieh, H. Vincent Poor

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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.

Original languageEnglish (US)
Article numbere2202235119
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number24
StatePublished - Jun 14 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General


  • concatenated quantum code
  • entanglement fidelity
  • entanglement-assisted quantum error-correction code
  • error-correction code
  • quantum Hamming bound

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