Approximate Degradable Quantum Channels

Sutter, D; Scholz, VB; Winter, A; Renner, R

Approximate Degradable Quantum Channels

Sutter, D Scholz, VB Winter, A

Renner, R

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2017, 63 (12), pp. 7832 - 7844
Issue Date:: 2017-12-01

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Field	Value	Language
dc.contributor.author	Sutter, D	en_US
dc.contributor.author	Scholz, VB	en_US
dc.contributor.author	Winter, A https://orcid.org/0000-0001-6344-4870	en_US
dc.contributor.author	Renner, R	en_US
dc.date.issued	2017-12-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2017, 63 (12), pp. 7832 - 7844	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/126818
dc.description.abstract	© 1963-2012 IEEE. Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact that a complementary channel can be obtained from the channel by applying a degrading channel. In this paper, we introduce the concept of approximate degradable channels, which satisfy this condition up to some finite ≥ 0. That is, there exists a degrading channel which upon composition with the channel is close in the diamond norm to the complementary channel. We show that for any fixed channel the smallest such can be efficiently determined via a semidefinite program. Moreover, these approximate degradable channels also approximately inherit all other properties of degradable channels. As an application, we derive improved upper bounds to the quantum and private classical capacity for certain channels of interest in quantum communication.	en_US
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2017.2754268	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	Approximate Degradable Quantum Channels	en_US
dc.type	Journal Article
utslib.citation.volume	12	en_US
utslib.citation.volume	63	en_US
utslib.for	1005 Communications Technologies	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	0906 Electrical and Electronic Engineering	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
utslib.copyright.status	closed_access
pubs.issue	12	en_US
pubs.publication-status	Published	en_US
pubs.volume	63	en_US

Abstract:

© 1963-2012 IEEE. Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact that a complementary channel can be obtained from the channel by applying a degrading channel. In this paper, we introduce the concept of approximate degradable channels, which satisfy this condition up to some finite ≥ 0. That is, there exists a degrading channel which upon composition with the channel is close in the diamond norm to the complementary channel. We show that for any fixed channel the smallest such can be efficiently determined via a semidefinite program. Moreover, these approximate degradable channels also approximately inherit all other properties of degradable channels. As an application, we derive improved upper bounds to the quantum and private classical capacity for certain channels of interest in quantum communication.

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http://hdl.handle.net/10453/126818