Catalytic quantum error correction

Brun, TA; Devetak, I; Hsieh, MH

Catalytic quantum error correction

Brun, TA Devetak, I Hsieh, MH

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2014, 60 (6), pp. 3073 - 3089
Issue Date:: 2014-01-01

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Field	Value	Language
dc.contributor.author	Brun, TA	en_US
dc.contributor.author	Devetak, I	en_US
dc.contributor.author	Hsieh, MH https://orcid.org/0000-0002-3396-8427	en_US
dc.date.issued	2014-01-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2014, 60 (6), pp. 3073 - 3089	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/43740
dc.description.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. © 1963-2012 IEEE.	en_US
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2014.2313559	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	Catalytic quantum error correction	en_US
dc.type	Journal Article
utslib.citation.volume	6	en_US
utslib.citation.volume	60	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	1005 Communications Technologies	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access
pubs.issue	6	en_US
pubs.publication-status	Published	en_US
pubs.volume	60	en_US

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. © 1963-2012 IEEE.

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