Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof

  • Authors:

  • Dong Yang;Karol Horodecki;Michał Horodecki;Paweł Horodecki;Jonathan Oppenheim;Wei Song

  • Affiliations:

  • Laboratory for Quantum Information, China Jiliang University, Hangzhou, Zhejiang, China;Institute of Informatics, University of Warsaw, Warsaw, Poland and Faculty of Mathematics, Physics and Computer Science, University of Gdansk, Gdansk, Poland;Institute of Theoretical Physics and Astrophysics, University of Gdansk, Gdansk, Poland;Faculty of Applied Physics and Mathematics, Technical University of Gdansk, Gdansk, Poland;Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK;School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou, China and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui, ...

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

Quantified Score

Hi-index 754.84

Visualization

Abstract

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.