  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.
