Stolze, JoachimChong, BoKeiter, Hellmut2008-06-062008-06-062005Chong, Bo; Keiter, Hellmut; Stolze, Joachim: Multiparticle entanglement and ranks of density matrices, preprint 2005, arXiv:quant-ph/0512199v1.http://hdl.handle.net/2003/25453http://dx.doi.org/10.17877/DE290R-2688Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we obtain necessary conditions for the separability of a given mixed state with respect to partitions of all particles of the system into subsets. The special case of pure states is discussed separately.en530Texthttp://arxiv.org/abs/quant-ph/0512199