Strassen's theorem for quantum couplings

Zhou, L; Ying, S; Yu, N; Ying, M

Strassen's theorem for quantum couplings

Zhou, L Ying, S Yu, N

Ying, M

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Publication Type:: Journal Article
Citation:: Theoretical Computer Science, 2020, 802 pp. 67 - 76
Issue Date:: 2020-01-08

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Field	Value	Language
dc.contributor.author	Zhou, L	en_US
dc.contributor.author	Ying, S	en_US
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032	en_US
dc.contributor.author	Ying, M https://orcid.org/0000-0003-4847-702X	en_US
dc.date.accessioned	2020-04-03T03:32:49Z
dc.date.available	2020-04-03T03:32:49Z
dc.date.issued	2020-01-08	en_US
dc.identifier.citation	Theoretical Computer Science, 2020, 802 pp. 67 - 76	en_US
dc.identifier.issn	0304-3975	en_US
dc.identifier.uri	http://hdl.handle.net/10453/139764
dc.description.abstract	© 2019 Elsevier B.V. Strassen's theorem for probabilistic couplings is a fundamental theorem in probability theory that can be used to bound the probability of an event in a distribution by the probability of an event in another distribution coupled with the first. It has been widely applied in computer science for analysis of random algorithms, machine learning and verification of security and privacy protocols. We extend the coupling techniques in probability theory to quantum systems. A quantum generalisation of the notion of lifting, a coupling under certain constraints, is introduced. Several interesting examples and basic properties of quantum couplings and liftings are presented. Finally, a quantum extension of Strassen's theorem is established.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP160101652
dc.relation	http://purl.org/au-research/grants/arc/DE180100156
dc.relation.ispartof	Theoretical Computer Science	en_US
dc.relation.isbasedon	10.1016/j.tcs.2019.08.026	en_US
dc.subject.classification	Computation Theory & Mathematics	en_US
dc.title	Strassen's theorem for quantum couplings	en_US
dc.type	Journal Article
utslib.citation.volume	802	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	08 Information and Computing Sciences	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
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US
pubs.volume	802	en_US

Abstract:

© 2019 Elsevier B.V. Strassen's theorem for probabilistic couplings is a fundamental theorem in probability theory that can be used to bound the probability of an event in a distribution by the probability of an event in another distribution coupled with the first. It has been widely applied in computer science for analysis of random algorithms, machine learning and verification of security and privacy protocols. We extend the coupling techniques in probability theory to quantum systems. A quantum generalisation of the notion of lifting, a coupling under certain constraints, is introduced. Several interesting examples and basic properties of quantum couplings and liftings are presented. Finally, a quantum extension of Strassen's theorem is established.

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http://hdl.handle.net/10453/139764