One-shot manipulation of entanglement for quantum channels

Understand

We show that the dynamic resource theory of quantum entanglement can be formulated using the superchannel theory.

• In this formulation, we identify the separable channels and the class of free superchannels that preserve channel separability as free resources, and choose the swap channels as dynamic entanglement golden units.
• Our first result is that the one-shot dynamic entanglement cost of a bipartite quantum channel under the free superchannels is bounded by the standard log-robustness of channels.
• The one-shot distillable dynamic entanglement of a bipartite quantum channel under the free superchannels is found to be bounded by a resource monotone that we construct from the hypothesis-testing relative entropy of channels with minimization over separable channels.