Entanglement-assisted concatenated quantum codes

TL;DR

This paper introduces entanglement-assisted concatenated quantum codes (EACQCs), demonstrating their advantages over standard codes, including better parameters, ability to beat bounds, and robustness with noisy entanglement, enhancing quantum communication and computation.

Contribution

The paper proposes EACQCs, a new class of quantum codes that outperform standard codes in various parameters and can operate effectively with noisy entanglement.

Findings

EACQCs can beat the nondegenerate Hamming bound for EAQECCs.

Several EACQCs have better parameters than existing QECCs and EAQECCs.

EACQCs outperform CQCs in entanglement fidelity when ebits are less noisy.

Abstract

Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show several advantages over the standard concatenated quantum codes (CQCs). Several families of EACQCs that, unlike standard CQCs, can beat the nondegenerate Hamming bound for entanglement-assisted quantum error correction codes (EAQECCs) are derived. Further, a number of EACQCs with better parameters than the best known standard quantum error correction codes (QECCs) and EAQECCs are also derived. In particular, several catalytic EACQCs with better parameters than the best known QECCs of the same length and net transmission are constructed. Furthermore, each catalytic EACQC consumes only one or two ebits. It is also shown that EACQCs make entanglement-assisted quantum communication possible even if the ebits are noisy. Finally, it is shown that EACQCs can outperform CQCs in entanglement fidelity over depolarizing channels if the ebits are less noisy than the qubits. Moreover, the threshold error probability of EACQCs is larger than that of CQCs when the error probability of ebits is sufficiently lower than that of qubits. Therefore EACQCs are not only competitive in quantum communication but also applicable in fault-tolerant quantum computation.