Separability of /n-particle mixed states: necessary and sufficient conditions in terms of linear maps

We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of n-1 particles. The method of construction of the maps on the basis of unextendible product bases is provided. The three-qubit problem is discussed in more details involving Bloch sphere parameters of qubit state.