Choi matrices, norms and entanglement associated with positive maps on matrix algebras

We study positive maps of B(K) into B(H) for finite-dimensional Hilbert spaces K and H. Our main emphasis is on how Choi matrices and estimates of their norms with respect to mapping cones reflect various properties of the maps. Special attention will be given to entanglement properties and k-positive maps, in particular tensor products of 2-positive maps. The latter problem is directly related to the question of n-copy distillability of quantum states, for which we obtain a partial result.