Entanglement-Saving Channels

Abstract

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 $\psi$ is said to be ES if its powers ${\psi }^n$ 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 which, not only preserve entanglement for all finite $n$, but which also sustain an explicitly not null level of entanglement in the asymptotic limit~$n\to \infty$. 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.

26 pages

References in corpus (3)

• Quantum channels and their entropic characteristics
• Entanglement-Breaking Indices
• Quantum channels with polytopic images and image additivity

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