期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 60, 期 6, 页码 3073-3089出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2313559
关键词
Quantum error-correcting code; entanglement; quantum information theory; father protocol
资金
- NSF [CCF-0448658, ECS-0507270, CCF-0524811, CCF-0545845]
- UTS Chancellors Post-Doctoral Research Fellowship
- UTS Early Career Researcher Grants Scheme
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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