Entanglement-saving channels

The set of Entanglement Saving (ES) quantum channels is introduced and characterized. These are completely positive, trace preserving transformations which when acting locally on a bipartite quantum system initially prepared into a maximally entangled configuration, preserve its entanglement even when applied an arbitrary number of times. In other words, a quantum channel ψ is said to be ES if its powers ψⁿ are not entanglement-breaking for all integers n. We also characterize the properties of the Asymptotic Entanglement Saving (AES) maps. These form a proper subset of the ES channels that is constituted by those maps that not only preserve entanglement for all finite n but which also sustain an explicitly not null level of entanglement in the asymptotic limit n → ∞. Structure theorems are provided for ES and for AES maps which yield an almost complete characterization of the former and a full characterization of the latter.