Quantum Strassen’s theorem

Friedland, S; Ge, J; Zhi, L

Quantum Strassen’s theorem

Friedland, S Ge, J Zhi, L

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Publisher:: World Scientific Pub Co Pte Lt
Publication Type:: Journal Article
Citation:: Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2020, 23, (03), pp. 2050020-2050020
Issue Date:: 2020-09

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Field	Value	Language
dc.contributor.author	Friedland, S
dc.contributor.author	Ge, J
dc.contributor.author	Zhi, L
dc.date.accessioned	2021-04-28T23:56:08Z
dc.date.available	2021-04-28T23:56:08Z
dc.date.issued	2020-09
dc.identifier.citation	Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2020, 23, (03), pp. 2050020-2050020
dc.identifier.issn	0219-0257
dc.identifier.issn	1793-6306
dc.identifier.uri	http://hdl.handle.net/10453/148514
dc.description.abstract	<jats:p> Strassen’s theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite, Strassen’s theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen’s theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen’s theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite-dimensional. </jats:p>
dc.language	en
dc.publisher	World Scientific Pub Co Pte Lt
dc.relation.ispartof	Infinite Dimensional Analysis, Quantum Probability and Related Topics
dc.relation.isbasedon	10.1142/s0219025720500204
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0102 Applied Mathematics, 0104 Statistics
dc.subject.classification	General Mathematics
dc.title	Quantum Strassen’s theorem
dc.type	Journal Article
utslib.citation.volume	23
utslib.for	0102 Applied Mathematics
utslib.for	0104 Statistics
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/Faculty of Engineering and Information Technology/School of Computer Science
utslib.copyright.status	closed_access	*
dc.date.updated	2021-04-28T23:56:06Z
pubs.issue	03
pubs.publication-status	Published
pubs.volume	23
utslib.citation.issue	03

Abstract:

Strassen’s theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite, Strassen’s theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen’s theorem in this case can be stated and solved using semidefinite programming. The aim of this paper is to give analogs of Strassen’s theorem to density trace class operators on a product of two separable Hilbert spaces, where at least one of the Hilbert spaces is infinite-dimensional.

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http://hdl.handle.net/10453/148514