When Does Noise Increase the Quantum Capacity?

Superactivation is the property that two channels with zero quantum capacity can be used together to yield a positive capacity. Here we demonstrate that this effect exists for a wide class of inequivalent channels, none of which can simulate each other. We also consider the case where one of two zero-capacity channels is applied, but the sender is ignorant of which one is applied. We find examples where the greater the entropy of mixing of the channels, the greater the lower bound for the capacity. Finally, we show that the effect of superactivation is rather generic by providing an example of superactivation using the depolarizing channel.

Figure 1

Nonconvexity of quantum capacity for $I_c(A⟩B)=\frac{1}{2}(1-\kappa )[\kappa -p(\kappa +2)+1]\log d$ when $d=2$ when the dimension of the shield subsystem tends to infinity.