  Entanglement lies at the root of quantum theory. It is a remarkable resource
that is generally believed to diminish when entangled systems interact with
their environment. On the contrary, we find that engaging a system with its
environment increases its ability to retain entanglement. The maximum rate of
retaining entanglement is given by the quantum channel capacity. We
counter-intuitively boost the quantum capacity of a channel by leaking almost
all quantum information to the channel's environment. This boost exploits
two-letter level non-additivity in the channel's coherent information. The
resulting non-additivity has a far larger magnitude and a qualitatively wider
extent than previously known. Our findings have a surprising implication for
quantum key distribution: maximum rates for key distribution can be boosted by
allowing leakage of information to the eavesdropping environment.
