Locally undetermined states, generalized schmidt decomposition, and application in deistributed comuting

Feng, Y; Duan, R; Ying, M

Locally undetermined states, generalized schmidt decomposition, and application in deistributed comuting

Feng, Y

Duan, R

Ying, M

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Publication Type:: Journal Article
Citation:: Quantum Information and Computation, 2009, 9 (11-12), pp. 0997 - 1012
Issue Date:: 2009-11-01

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Field	Value	Language
dc.contributor.author	Feng, Y https://orcid.org/0000-0002-3097-3896	en_US
dc.contributor.author	Duan, R https://orcid.org/0000-0002-4388-7487	en_US
dc.contributor.author	Ying, M https://orcid.org/0000-0003-4847-702X	en_US
dc.date.issued	2009-11-01	en_US
dc.identifier.citation	Quantum Information and Computation, 2009, 9 (11-12), pp. 0997 - 1012	en_US
dc.identifier.issn	1533-7146	en_US
dc.identifier.uri	http://hdl.handle.net/10453/11787
dc.description.abstract	Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit 'high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computing. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state. © Rinton Press.	en_US
dc.relation.ispartof	Quantum Information and Computation	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Locally undetermined states, generalized schmidt decomposition, and application in deistributed comuting	en_US
dc.type	Journal Article
utslib.citation.volume	11-12	en_US
utslib.citation.volume	9	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
utslib.for	0206 Quantum Physics	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	open_access
pubs.issue	11-12	en_US
pubs.publication-status	Published	en_US
pubs.volume	9	en_US

Abstract:

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit 'high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computing. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state. © Rinton Press.

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http://hdl.handle.net/10453/11787