Zero-error communication via quantum channels and a quantum Lovász script v sign-function

Duan, R; Severini, S; Winter, A

Zero-error communication via quantum channels and a quantum Lovász script v sign-function

Duan, R

Severini, S Winter, A

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Publication Type:: Conference Proceeding
Citation:: IEEE International Symposium on Information Theory - Proceedings, 2011, pp. 64 - 68
Issue Date:: 2011-10-26

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Field	Value	Language
dc.contributor.author	Duan, R https://orcid.org/0000-0002-4388-7487	en_US
dc.contributor.author	Severini, S	en_US
dc.contributor.author	Winter, A https://orcid.org/0000-0001-6344-4870	en_US
dc.date.issued	2011-10-26	en_US
dc.identifier.citation	IEEE International Symposium on Information Theory - Proceedings, 2011, pp. 64 - 68	en_US
dc.identifier.isbn	9781457705953	en_US
dc.identifier.uri	http://hdl.handle.net/10453/30800
dc.description.abstract	We study the quantum channel version of Shannon's zero-error capacity problem. Motivated by recent progress on this question, we propose to consider a certain linear space operators as the quantum generalisation of the adjacency matrix, in terms of which the plain, quantum and entanglement-assisted capacity can be formulated, and for which we show some new basic properties. Most importantly, we define a quantum version of Lovász' famous script v sign function, as the norm-completion (or stabilisation) of a "naive" generalisation of script v sign. We go on to show that this function upper bounds the number of entanglement-assisted zero-error messages, that it is given by a semidefinite programme, whose dual we write down explicitly, and that it is multiplicative with respect to the natural (strong) graph product. We explore various other properties of the new quantity, which reduces to Lovász' original script v sign in the classical case, give several applications, and propose to study the linear spaces of operators associated to channels as "non-commutative graphs", using the language of operator systems and Hilbert modules. © 2011 IEEE.	en_US
dc.relation.ispartof	IEEE International Symposium on Information Theory - Proceedings	en_US
dc.relation.isbasedon	10.1109/ISIT.2011.6034211	en_US
dc.title	Zero-error communication via quantum channels and a quantum Lovász script v sign-function	en_US
dc.type	Conference Proceeding
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
dc.location.activity	St Petersburg, Russia
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	closed_access
pubs.publication-status	Published	en_US

Abstract:

We study the quantum channel version of Shannon's zero-error capacity problem. Motivated by recent progress on this question, we propose to consider a certain linear space operators as the quantum generalisation of the adjacency matrix, in terms of which the plain, quantum and entanglement-assisted capacity can be formulated, and for which we show some new basic properties. Most importantly, we define a quantum version of Lovász' famous script v sign function, as the norm-completion (or stabilisation) of a "naive" generalisation of script v sign. We go on to show that this function upper bounds the number of entanglement-assisted zero-error messages, that it is given by a semidefinite programme, whose dual we write down explicitly, and that it is multiplicative with respect to the natural (strong) graph product. We explore various other properties of the new quantity, which reduces to Lovász' original script v sign in the classical case, give several applications, and propose to study the linear spaces of operators associated to channels as "non-commutative graphs", using the language of operator systems and Hilbert modules. © 2011 IEEE.

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http://hdl.handle.net/10453/30800