Classification of multiqubit mixed states: Separability and distillability properties

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 4, 2000, Pages 11-

  Dur W ^a   Cirac, J I ^a  

^a UNIVERSITY OF INNSBRUCK   (Austria)

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EID: 84873367192     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.61.042314     Document Type: Article

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34. For example, we have that the following combination is in principle allowed: The state (Formula presented) is 4-inseparable, 3-inseparable with respect to all possible 3-partite splits (3a)–(3f), but 2-separable with respect to all possible bipartite splits (2a)–(2g). On the other hand, we have that the following combination is not allowed: (Formula presented) is 4-inseparable, 3-separable with respect to all possible 3-partite splits (3a)–(3f) and 2-separable with respect to the bipartite splits (2b)–(2g), but 2-inseparable with respect to the bipartite split (2a). Since, e.g., the 3-separability with respect to the 3-partite split (3a) already implies the 2-separability with respect to the bipartite split (2a) (see Fig. 22), it follows that this configuration is impossible and thus forbidden.
35. In R. Schack and C. M. Caves, e-print quant-ph/9904109, it was independently shown using different methods that for (Formula presented), the state (Formula presented) is separable for (Formula presented). For larger N however, only weaker bounds were obtained.