Allowing leakage can increase quantum transmission

Entanglement and quantum information lie at the root of quantum theory. These remarkable resources are generally believed to diminish when systems carrying them interact with their environment. By contrast, we find that engaging a system with its environment can increases its ability to carry quantum information. The maximum rate of transmission is given by the quantum channel capacity. We counter-intuitively boost this capacity of a channel by allowing it to leak almost all quantum information to the channel's environment. We conceptually and numerically explain this boost to arise from two-letter level super-additivity in the channel's coherent information. Such super-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.