Moderate Deviation Expansion for Fully Quantum Tasks

Ramakrishnan, N; Tomamichel, M; Berta, M

Moderate Deviation Expansion for Fully Quantum Tasks

Ramakrishnan, N Tomamichel, M

Berta, M

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2023, 69, (8), pp. 5041-5059
Issue Date:: 2023-08-01

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Field	Value	Language
dc.contributor.author	Ramakrishnan, N
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329
dc.contributor.author	Berta, M
dc.date.accessioned	2024-05-06T04:44:26Z
dc.date.available	2024-05-06T04:44:26Z
dc.date.issued	2023-08-01
dc.identifier.citation	IEEE Transactions on Information Theory, 2023, 69, (8), pp. 5041-5059
dc.identifier.issn	0018-9448
dc.identifier.issn	1557-9654
dc.identifier.uri	http://hdl.handle.net/10453/178679
dc.description.abstract	The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, where the communication cost approaches a capacity-like quantity and the error vanishes at the same time. We find exact characterisations of these trade-offs for a variety of fully quantum communication tasks, including quantum source coding, quantum state splitting, entanglement-assisted quantum channel coding, and entanglement-assisted quantum channel simulation. The main technical tool we derive is a tight relation between the partially smoothed max-information and the hypothesis testing relative entropy. This allows us to obtain the expansion of the partially smoothed max-information for i.i.d. states in the moderate deviation regime.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation.ispartof	IEEE Transactions on Information Theory
dc.relation.isbasedon	10.1109/TIT.2023.3262145
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies
dc.subject.classification	Networking & Telecommunications
dc.subject.classification	4006 Communications engineering
dc.subject.classification	4613 Theory of computation
dc.title	Moderate Deviation Expansion for Fully Quantum Tasks
dc.type	Journal Article
utslib.citation.volume	69
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	1005 Communications Technologies
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	*
dc.date.updated	2024-05-06T04:44:25Z
pubs.issue	8
pubs.publication-status	Published
pubs.volume	69
utslib.citation.issue	8

Abstract:

The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, where the communication cost approaches a capacity-like quantity and the error vanishes at the same time. We find exact characterisations of these trade-offs for a variety of fully quantum communication tasks, including quantum source coding, quantum state splitting, entanglement-assisted quantum channel coding, and entanglement-assisted quantum channel simulation. The main technical tool we derive is a tight relation between the partially smoothed max-information and the hypothesis testing relative entropy. This allows us to obtain the expansion of the partially smoothed max-information for i.i.d. states in the moderate deviation regime.

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http://hdl.handle.net/10453/178679