Rank reduction for the local consistency problem

Chen, J; Ji, Z; Klyachko, A; Kribs, DW; Zeng, B

Rank reduction for the local consistency problem

Chen, J Ji, Z

Klyachko, A Kribs, DW Zeng, B

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Publication Type:: Journal Article
Citation:: Journal of Mathematical Physics, 2012, 53 (2)
Issue Date:: 2012-02-02

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Field	Value	Language
dc.contributor.author	Chen, J	en_US
dc.contributor.author	Ji, Z https://orcid.org/0000-0002-7659-3178	en_US
dc.contributor.author	Klyachko, A	en_US
dc.contributor.author	Kribs, DW	en_US
dc.contributor.author	Zeng, B	en_US
dc.date.issued	2012-02-02	en_US
dc.identifier.citation	Journal of Mathematical Physics, 2012, 53 (2)	en_US
dc.identifier.issn	0022-2488	en_US
dc.identifier.uri	http://hdl.handle.net/10453/114990
dc.description.abstract	We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank. © 2012 American Institute of Physics.	en_US
dc.relation.ispartof	Journal of Mathematical Physics	en_US
dc.relation.isbasedon	10.1063/1.3685644	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Rank reduction for the local consistency problem	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	53	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	02 Physical 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	open_access
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	53	en_US

Abstract:

We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank. © 2012 American Institute of Physics.

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http://hdl.handle.net/10453/114990