  We first investigate the one-shot static entanglement cost to simulate a
bipartite quantum channel under the set of non-entangling channels. The lower
bound on the static entanglement cost is given by the generalized robustness of
the target channel as well as the robust-generating power of the channel, which
implies that the cost necessary to generate a bipartite quantum channel might
not be retrievable in general. Next, we conceive a set of quantum channels that
extends the set of non-entangling channels. We find out that the one-shot
static entanglement cost under the extended set of channels is given by the
channel's standard log-robustness. This gives the one-shot dynamic entanglement
cost under a set of free superchannels that do not generate dynamic
entanglement resource; the extended set is shown to be equivalent to the set of
free superchannels.

Quantum Physics