  Sharing entanglement across quantum interconnects is fundamental for quantum
information processing. We discuss a practical setting where this interconnect,
modeled by a quantum channel, is used once with the aim of sharing high
fidelity entanglement. For any channel, we provide methods to easily find both
this maximum fidelity and optimal inputs that achieve it. Unlike most metrics
for sharing entanglement, this maximum fidelity can be shown to be
multiplicative. This ensures a complete understanding in the sense that the
maximum fidelity and optimal inputs found in our one-shot setting extend even
when the channel is used multiple times, possibly with other channels. Optimal
inputs need not be fully entangled. We find the minimum entanglement in these
optimal inputs can even vary discontinuously with channel noise. Generally,
noise parameters are hard to identify and remain unknown for most channels.
However, for all qubit channels with qubit environments, we provide a rigorous
noise parametrization which we explain in-terms of no-cloning. This noise
parametrization and a channel representation we call the standard Kraus
decomposition have pleasing properties that make them both useful more
generally.
