Squashed Entanglement for Multipartite States and Entanglement Measures Based on the Mixed Convex Roof

New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states. One is a generalization of the squashed entanglement where one takes the mutual information of parties conditioned on the...

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Bibliographic Details
Published in:IEEE transactions on information theory 2009-07, Vol.55 (7), p.3375-3387
Main Authors: Dong Yang, Horodecki, K., Horodecki, M., Horodecki, P., Oppenheim, J., Wei Song
Format: Article
Language:English
Subjects:
Applied sciences
C-squashed entanglement
Cryptography
Decomposition
Density
Density measurement
Entanglement
Entropy
Exact sciences and technology
Extraterrestrial measurements
Infimum
Information processing
Information theory
Information, signal and communications theory
Mathematics
Matrix decomposition
Measurement
Measurement standards
mixed convex roof
multipartite distillable key
Mutual information
Optimization
Optimization methods
Optimization techniques
Physics
Roofs
Signal and communications theory
squashed entanglement
Telecommunications and information theory
Upper bound
Upper bounds
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Summary:New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states. One is a generalization of the squashed entanglement where one takes the mutual information of parties conditioned on the state's extension and takes the infimum over such extensions. Additivity of the multipartite squashed entanglement is proved for both versions of the multipartite information which turn out to be related. The second one is based on taking classical extensions. This scheme is generalized, which enables to construct measures of entanglement based on the mixed convex roof of a quantity, which in contrast to the standard convex roof method involves optimization over all decompositions of a density matrix rather than just the decompositions into pure states. As one of the possible applications of these results we prove that any multipartite monotone is an upper bound on the amount of multipartite distillable key. The findings are finally related to analogous results in classical key agreement.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2009.2021373