Optimal extensions of resource measures and their applications

Gour, G; Tomamichel, M

Optimal extensions of resource measures and their applications

Gour, G Tomamichel, M

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Publisher:: American Physical Society (APS)
Publication Type:: Journal Article
Citation:: Physical Review A, 2020, 102, (6), pp. 062401
Issue Date:: 2020-12-01

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Field	Value	Language
dc.contributor.author	Gour, G
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329
dc.date.accessioned	2021-03-22T20:01:42Z
dc.date.available	2021-03-22T20:01:42Z
dc.date.issued	2020-12-01
dc.identifier.citation	Physical Review A, 2020, 102, (6), pp. 062401
dc.identifier.issn	2469-9926
dc.identifier.issn	2469-9934
dc.identifier.uri	http://hdl.handle.net/10453/147446
dc.description.abstract	© 2020 American Physical Society. We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various applications of our framework. We show that any relative entropy (i.e., an additive function on pairs of quantum states that satisfies the data processing inequality) must be bounded by the min and max relative entropies. We prove that the generalized trace distance, the generalized fidelity, and the purified distance are optimal extensions. And in entanglement theory we introduce a technique to extend pure-state entanglement measures to mixed bipartite states.
dc.language	en
dc.publisher	American Physical Society (APS)
dc.relation.ispartof	Physical Review A
dc.relation.isbasedon	https://dx.doi.org/10.1103/PhysRevA.102.062401
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	01 Mathematical Sciences, 02 Physical Sciences, 03 Chemical Sciences
dc.subject.classification	General Physics
dc.title	Optimal extensions of resource measures and their applications
dc.type	Journal Article
utslib.citation.volume	102
utslib.for	01 Mathematical Sciences
utslib.for	02 Physical Sciences
utslib.for	03 Chemical Sciences
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access	*
dc.date.updated	2021-03-22T20:01:40Z
pubs.issue	6
pubs.publication-status	Published
pubs.volume	102
utslib.citation.issue	6

Abstract:

© 2020 American Physical Society. We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various applications of our framework. We show that any relative entropy (i.e., an additive function on pairs of quantum states that satisfies the data processing inequality) must be bounded by the min and max relative entropies. We prove that the generalized trace distance, the generalized fidelity, and the purified distance are optimal extensions. And in entanglement theory we introduce a technique to extend pure-state entanglement measures to mixed bipartite states.

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http://hdl.handle.net/10453/147446