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Catalytic Quantum Error Correction
We develop the theory of entanglement-assisted quantum error-correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to preshared entanglement. Conventional stabilizer codes are equivalent to self-orthogonal symplectic codes....
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Published in: | IEEE transactions on information theory 2014-06, Vol.60 (6), p.3073-3089 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | We develop the theory of entanglement-assisted quantum error-correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to preshared entanglement. Conventional stabilizer codes are equivalent to self-orthogonal symplectic codes. In contrast, EAQEC codes do not require self-orthogonality, which greatly simplifies their construction. We show how any classical binary or quaternary block code can be made into an EAQEC code. We provide a table of best known EAQEC codes with code length up to 10. With the self-orthogonality constraint removed, we see that the distance of an EAQEC code can be better than any standard quantum error-correcting code with the same fixed net yield. In a quantum computation setting, EAQEC codes give rise to catalytic quantum codes, which assume a subset of the qubits are noiseless. We also give an alternative construction of EAQEC codes by making classical entanglement-assisted codes coherent. |
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ISSN: | 0018-9448 1557-9654 |
DOI: | 10.1109/TIT.2014.2313559 |