\([[3, 1, 3;2]]\) EA code

\([[3, 1, 3;2]]\) EA code[1]

Description

Distance-three EA stabilizer code encoding one logical qubit and using two ebits. It is the smallest example of an EA code correcting an arbitrary single-qubit error.

Cousins

Entanglement-assisted (EA) QECC— The \([[3, 1, 3;2]]\) EA code is the first EA code.
\([[5,1,3]]\) Five-qubit perfect code— The \([[3, 1, 3;2]]\) EA code and the five-qubit code have the same stabilizers [2,3].
Small-distance qubit stabilizer code

Member of code lists

Primary Hierarchy

Quantum Domain

Qubit Kingdom

EAOA qubit codeQuantum

EA qubit codeEAQECC Quantum

EA qubit stabilizer codeEAQECC Quantum

Parents

EA qubit stabilizer code

\([[3, 1, 3;2]]\) EA code

References

[1]: G. Bowen, “Entanglement required in achieving entanglement-assisted channel capacities”, Physical Review A 66, (2002) arXiv:quant-ph/0205117 DOI
[2]: T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting Quantum Errors with Entanglement”, Science 314, 436 (2006) arXiv:quant-ph/0610092 DOI
[3]: J. Fan, J. Li, Y. Zhou, M.-H. Hsieh, and H. V. Poor, “Entanglement-assisted concatenated quantum codes”, Proceedings of the National Academy of Sciences 119, (2022) arXiv:2202.08084 DOI

Page edit log

Victor V. Albert (2026-06-08) — most recent
Victor V. Albert (2024-07-04)

Cite as:

“\([[3, 1, 3;2]]\) EA code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/ea_3_1_3-2, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/eaoa/ea/ea_stabilizer/ea_3_1_3-2.yml.