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Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
Abstract
New measures of multipartite entanglement are constructedbased on two definitions of multipartite information anddifferent methods of optimizing over extensions of the states. Oneis a generalization of the squashed entanglement where one takesthe mutual information of parties conditioned on the state's extensionand takes the infimum over such extensions. Additivity ofthe multipartite squashed entanglement is proved for both versionsof the multipartite information which turn out to be related. Thesecond one is based on taking classical extensions. This scheme isgeneralized, which enables to construct measures of entanglementbased on the mixed convex roof of a quantity, which in contrastto the standard convex roof method involves optimization over alldecompositions of a density matrix rather than just the decompositionsinto pure states. As one of the possible applications of theseresults we prove that any multipartite monotone is an upper boundon the amount of multipartite distillable key. The findings are finallyrelated to analogous results in classical key agreement.
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
IEEE TRANSACTIONS ON INFORMATION THEORY
no. 55,
pages 3375 - 3387,
ISSN: 0018-9448 - Language:
- English
- Publication year:
- 2009
- Bibliographic description:
- Yang D., Horodecki K., Horodecki M., Horodecki P., Oppenheim J., Song W.: Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof// IEEE TRANSACTIONS ON INFORMATION THEORY. -Vol. 55, nr. iss. 7, July (2009), s.3375-3387
- Verified by:
- Gdańsk University of Technology
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