Tensor rank and stochastic entanglement catalysis for multipartite pure states

Chen, L; Chitambar, E; Duan, R; Ji, Z; Winter, A

Tensor rank and stochastic entanglement catalysis for multipartite pure states

Chen, L Chitambar, E Duan, R

Ji, Z

Winter, A

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Publication Type:: Journal Article
Citation:: Physical Review Letters, 2010, 105 (20)
Issue Date:: 2010-11-08

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Field	Value	Language
dc.contributor.author	Chen, L	en_US
dc.contributor.author	Chitambar, E	en_US
dc.contributor.author	Duan, R https://orcid.org/0000-0002-4388-7487	en_US
dc.contributor.author	Ji, Z https://orcid.org/0000-0002-7659-3178	en_US
dc.contributor.author	Winter, A https://orcid.org/0000-0001-6344-4870	en_US
dc.date.issued	2010-11-08	en_US
dc.identifier.citation	Physical Review Letters, 2010, 105 (20)	en_US
dc.identifier.issn	0031-9007	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8255
dc.description.abstract	The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state \|W3=1√3(\|100+\|010+\|001) and its N-partite generalization \|WN. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of \|W3 have a rank of either 15 or 16, (ii) two copies of \|WN have a rank of 3N-2, and (iii) n copies of \|WN have a rank of O(N). A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple-copy bunches or when assisted by some catalyzing state. This effect is impossible for bipartite pure states. © 2010 The American Physical Society.	en_US
dc.relation.ispartof	Physical Review Letters	en_US
dc.relation.isbasedon	10.1103/PhysRevLett.105.200501	en_US
dc.subject.classification	General Physics	en_US
dc.title	Tensor rank and stochastic entanglement catalysis for multipartite pure states	en_US
dc.type	Journal Article
utslib.citation.volume	20	en_US
utslib.citation.volume	105	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	02 Physical Sciences	en_US
utslib.for	09 Engineering	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.issue	20	en_US
pubs.publication-status	Published	en_US
pubs.volume	105	en_US

Abstract:

The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state |W3=1√3(|100+|010+|001) and its N-partite generalization |WN. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of |W3 have a rank of either 15 or 16, (ii) two copies of |WN have a rank of 3N-2, and (iii) n copies of |WN have a rank of O(N). A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple-copy bunches or when assisted by some catalyzing state. This effect is impossible for bipartite pure states. © 2010 The American Physical Society.

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http://hdl.handle.net/10453/8255