Title :
Catalytic Quantum Error Correction
Author :
Brun, Todd A. ; Devetak, Igor ; Min-Hsiu Hsieh
Author_Institution :
Ming Hsieh Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA
Abstract :
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.
Keywords :
block codes; error correction codes; orthogonal codes; quantum entanglement; EAQEC code; binary block code; entanglement-assisted quantum error-correcting codes; preshared entanglement; quaternary block code; self-orthogonal symplectic codes; self-orthogonality constraint; Encoding; Protocols; Quantum entanglement; Standards; Vectors; Quantum error-correcting code; and father protocol; entanglement; quantum information theory;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2014.2313559