  We fully characterize bipartite entanglement-annihilating (EA) channels that
destroy entanglement of any state shared by subsystems and, thus, should be
avoided in any entanglement-enabled experiment. Our approach relies on
extending the problem to EA positive maps, the cone of which remains invariant
under concatenation with partially positive maps. Due to this invariancy,
positive EA maps adopt a well characterization and their intersection with
completely positive trace-preserving maps results in the set of EA channels. In
addition to a general description, we also provide sufficient operational
criteria revealing EA channels. They have a clear physical meaning since the
processes involved contain stages of classical information transfer for
subsystems. We demonstrate the applicability of derived criteria for local and
global depolarizing noises, and specify corresponding noise levels beyond which
any initial state becomes disentangled after passing the channel. The
robustness of some entangled states is discussed.
