Semidefinite Programming Converse Bounds for Quantum Communication

Wang, X; Fang, K; Duan, R

Semidefinite Programming Converse Bounds for Quantum Communication

Wang, X

Fang, K

Duan, R

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2019, 65 (4), pp. 2583 - 2592
Issue Date:: 2019-04-01

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Field	Value	Language
dc.contributor.author	Wang, X https://orcid.org/0000-0002-0641-3186	en_US
dc.contributor.author	Fang, K https://orcid.org/0000-0002-9232-6846	en_US
dc.contributor.author	Duan, R https://orcid.org/0000-0002-4388-7487	en_US
dc.date.accessioned	2020-04-17T00:51:45Z
dc.date.available	2020-04-17T00:51:45Z
dc.date.issued	2019-04-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2019, 65 (4), pp. 2583 - 2592	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/140059
dc.description.abstract	© 2018 IEEE. We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of quantum information that can be transmitted over a single use of a quantum channel, which improve the previous bound from [Tomamichel/Berta/Renes, Nat. Commun. 7, 2016]. As applications, we study quantum communication over depolarizing channels and amplitude damping channels with finite resources. Second, we find an SDP-strong converse bound for the quantum capacity of an arbitrary quantum channel, which means the fidelity of any sequence of codes with a rate exceeding this bound will vanish exponentially fast as the number of channel uses increases. Furthermore, we prove that the SDP-strong converse bound improves the partial transposition bound introduced by Holevo and Werner. Third, we prove that this SDP strong converse bound is equal to the so-called max-Rains information, which is an analog to the Rains information introduced in [Tomamichel/Wilde/Winter, IEEE Trans. Inf. Theory 63:715, 2017]. Our SDP strong converse bound is weaker than the Rains information, but it is efficiently computable for general quantum channels.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP120103776
dc.relation	http://purl.org/au-research/grants/arc/FT120100449
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2018.2874031	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	Semidefinite Programming Converse Bounds for Quantum Communication	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	65	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
pubs.organisational-group	/University of Technology Sydney/Students
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	65	en_US

Abstract:

© 2018 IEEE. We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of quantum information that can be transmitted over a single use of a quantum channel, which improve the previous bound from [Tomamichel/Berta/Renes, Nat. Commun. 7, 2016]. As applications, we study quantum communication over depolarizing channels and amplitude damping channels with finite resources. Second, we find an SDP-strong converse bound for the quantum capacity of an arbitrary quantum channel, which means the fidelity of any sequence of codes with a rate exceeding this bound will vanish exponentially fast as the number of channel uses increases. Furthermore, we prove that the SDP-strong converse bound improves the partial transposition bound introduced by Holevo and Werner. Third, we prove that this SDP strong converse bound is equal to the so-called max-Rains information, which is an analog to the Rains information introduced in [Tomamichel/Wilde/Winter, IEEE Trans. Inf. Theory 63:715, 2017]. Our SDP strong converse bound is weaker than the Rains information, but it is efficiently computable for general quantum channels.

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http://hdl.handle.net/10453/140059