Second order refinements for the classical capacity of quantum channels with separable input states

Tomamichel, M; Tan, VYF

Second order refinements for the classical capacity of quantum channels with separable input states

Tomamichel, M

Tan, VYF

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Publication Type:: Conference Proceeding
Citation:: IEEE International Symposium on Information Theory - Proceedings, 2014, pp. 141 - 145
Issue Date:: 2014-01-01

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Field	Value	Language
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329	en_US
dc.contributor.author	Tan, VYF	en_US
dc.date.issued	2014-01-01	en_US
dc.identifier.citation	IEEE International Symposium on Information Theory - Proceedings, 2014, pp. 141 - 145	en_US
dc.identifier.isbn	9781479951864	en_US
dc.identifier.issn	2157-8095	en_US
dc.identifier.uri	http://hdl.handle.net/10453/119841
dc.description.abstract	We study the non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of information that can be transmitted when the channel is used a finite number of times and a finite average decoding error is permissible. We show that, if we restrict the encoder to use ensembles of separable states, the non-asymptotic fundamental limit admits a Gaussian approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the number of channel uses tends to infinity. To do so, several important properties of quantum information quantities, such as the capacity-achieving output state, the divergence radius, and the channel dispersion, are generalized from their classical counterparts. Further, we exploit a close relation between classical-quantum channel coding and quantum binary hypothesis testing and rely on recent progress in the non-asymptotic characterization of quantum hypothesis testing and its Gaussian approximation. © 2014 IEEE.	en_US
dc.relation.ispartof	IEEE International Symposium on Information Theory - Proceedings	en_US
dc.relation.isbasedon	10.1109/ISIT.2014.6874811	en_US
dc.title	Second order refinements for the classical capacity of quantum channels with separable input states	en_US
dc.type	Conference Proceeding
utslib.for	0802 Computation Theory and Mathematics	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/Faculty of Engineering and Information Technology/School of Computer Science
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 non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of information that can be transmitted when the channel is used a finite number of times and a finite average decoding error is permissible. We show that, if we restrict the encoder to use ensembles of separable states, the non-asymptotic fundamental limit admits a Gaussian approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the number of channel uses tends to infinity. To do so, several important properties of quantum information quantities, such as the capacity-achieving output state, the divergence radius, and the channel dispersion, are generalized from their classical counterparts. Further, we exploit a close relation between classical-quantum channel coding and quantum binary hypothesis testing and rely on recent progress in the non-asymptotic characterization of quantum hypothesis testing and its Gaussian approximation. © 2014 IEEE.

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