  Absolutely separable states $\varrho$ remain separable under arbitrary
unitary transformations $U \varrho U^{\dag}$. By example of a three qubit
system we show that in multipartite scenario neither full separability implies
bipartite absolute separability nor the reverse statement holds. The main goal
of the paper is to analyze quantum maps resulting in absolutely separable
output states. Such absolutely separating maps affect the states in a way, when
no Hamiltonian dynamics can make them entangled afterwards. We study general
properties of absolutely separating maps and channels with respect to
bipartitions and multipartitions and show that absolutely separating maps are
not necessarily entanglement breaking. We examine stability of absolutely
separating maps under tensor product and show that $\Phi^{\otimes N}$ is
absolutely separating for any $N$ if and only if $\Phi$ is the tracing map.
Particular results are obtained for families of local unital multiqubit
channels, global generalized Pauli channels, and combination of identity,
transposition, and tracing maps acting on states of arbitrary dimension. We
also study the interplay between local and global noise components in
absolutely separating bipartite depolarizing maps and discuss the input states
with high resistance to absolute separability.
