Open Systems & Information Dynamics

, Volume 13, Issue 1, pp 103–111 | Cite as

Separability of Mixed Quantum States: Linear Contractions and Permutation Criteria

  • Michał Horodecki
  • Paweł Horodecki
  • Ryszard Horodecki


Recently, a powerful separability criterion was introduced by O. Rudolf in [5] and by K. Chen et al. in [6] – basing on realignment of elements of density matrix. Composing the main idea behind the above criterion and the necessary and sufficient condition in terms of positive maps, we provide a characterization of separable states by means of linear contractions. The latter need not be positive maps. We extend the idea to multipartite systems, and find that, somewhat suprisingly, partial realigment (unlike partial transposition) can detect genuinely tri-parite entanglement. We generalize it by introducing a family of so called permutation separability criteria for multipartite states. Namely, any permutation of indices of density matrix written in product basis leads to a separability criterion. Partial transpose and realignment criterion are special cases of permutation criteria.


Statistical Physic Mechanical Engineer System Theory Quantum State Density Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Michał Horodecki
    • 1
  • Paweł Horodecki
    • 2
  • Ryszard Horodecki
    • 1
  1. 1.Institute of Theoretical Physics and AstrophysicsUniversity of GdańskGdańskPoland
  2. 2.Faculty of Applied Physics and MathematicsTechnical University of GdańskPoland

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