When is the chernoff exponent for quantum operations finite?

Yu, N; Zhou, L

When is the chernoff exponent for quantum operations finite?

Yu, N

Zhou, L

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2021, 67, (7), pp. 4517-4523
Issue Date:: 2021-07-01

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Field	Value	Language
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032
dc.contributor.author	Zhou, L
dc.date.accessioned	2022-03-31T03:54:30Z
dc.date.available	2022-03-31T03:54:30Z
dc.date.issued	2021-07-01
dc.identifier.citation	IEEE Transactions on Information Theory, 2021, 67, (7), pp. 4517-4523
dc.identifier.issn	0018-9448
dc.identifier.issn	1557-9654
dc.identifier.uri	http://hdl.handle.net/10453/155762
dc.description.abstract	We consider the problem of testing two hypotheses of quantum operations in a setting of many uses where an arbitrary prior probability distribution is given. The Chernoff exponent for quantum operations is investigated to track the minimal average error probability of discriminating two quantum operations asymptotically. We answer the question, 'When is the Chernoff exponent for quantum operations finite?' We show that either two quantum operations can be perfectly distinguished with finite uses, or the minimal discrimination error decays exponentially with respect to the number of uses asymptotically. That is, the Chernoff exponent is finite if and only if the quantum operations can not be perfectly distinguished with finite uses. This rules out the possibility of super-exponential decay of error probability. Upper bounds of the Chernoff exponent for quantum operations are provided.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation	http://purl.org/au-research/grants/arc/DE180100156
dc.relation.ispartof	IEEE Transactions on Information Theory
dc.relation.isbasedon	10.1109/TIT.2021.3067924
dc.rights	info:eu-repo/semantics/embargoedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies
dc.subject.classification	Networking & Telecommunications
dc.title	When is the chernoff exponent for quantum operations finite?
dc.type	Journal Article
utslib.citation.volume	67
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
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access	*
utslib.copyright.embargo	2023-07-31T00:00:00+1000Z
dc.date.updated	2022-03-31T03:54:29Z
pubs.issue	7
pubs.publication-status	Published
pubs.volume	67
utslib.citation.issue	7

Abstract:

We consider the problem of testing two hypotheses of quantum operations in a setting of many uses where an arbitrary prior probability distribution is given. The Chernoff exponent for quantum operations is investigated to track the minimal average error probability of discriminating two quantum operations asymptotically. We answer the question, 'When is the Chernoff exponent for quantum operations finite?' We show that either two quantum operations can be perfectly distinguished with finite uses, or the minimal discrimination error decays exponentially with respect to the number of uses asymptotically. That is, the Chernoff exponent is finite if and only if the quantum operations can not be perfectly distinguished with finite uses. This rules out the possibility of super-exponential decay of error probability. Upper bounds of the Chernoff exponent for quantum operations are provided.

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http://hdl.handle.net/10453/155762