Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels

Tomamichel, M; Tan, VYF

Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels

Tomamichel, M

Tan, VYF

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Publication Type:: Journal Article
Citation:: Communications in Mathematical Physics, 2015, 338 (1), pp. 103 - 137
Issue Date:: 2015-08-01

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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	2015-08-01	en_US
dc.identifier.citation	Communications in Mathematical Physics, 2015, 338 (1), pp. 103 - 137	en_US
dc.identifier.issn	0010-3616	en_US
dc.identifier.uri	http://hdl.handle.net/10453/119331
dc.description.abstract	© 2015, Springer-Verlag Berlin Heidelberg. We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite number of times and a fixed, non-vanishing average error is permissible. In this work we consider the classical capacity of quantum channels that are image-additive, including all classical to quantum channels, as well as the product state capacity of arbitrary quantum channels. In both cases we show that the non-asymptotic fundamental limit admits a second-order approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the blocklength tends to infinity. The behavior is governed by a new channel parameter, called channel dispersion, for which we provide a geometrical interpretation.	en_US
dc.relation.ispartof	Communications in Mathematical Physics	en_US
dc.relation.isbasedon	10.1007/s00220-015-2382-0	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	338	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	0206 Quantum Physics	en_US
utslib.for	0101 Pure 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.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	338	en_US

Abstract:

© 2015, Springer-Verlag Berlin Heidelberg. We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite number of times and a fixed, non-vanishing average error is permissible. In this work we consider the classical capacity of quantum channels that are image-additive, including all classical to quantum channels, as well as the product state capacity of arbitrary quantum channels. In both cases we show that the non-asymptotic fundamental limit admits a second-order approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the blocklength tends to infinity. The behavior is governed by a new channel parameter, called channel dispersion, for which we provide a geometrical interpretation.

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http://hdl.handle.net/10453/119331