The quantum capacity of a channel is a measure of its ability to reliably transmit quantum information in the asymptotic memoryless setting. In 2008, Smith and Yard demonstrated the striking phenomenon of superactivation, where two quantum channels — each individually incapable of transmitting quantum information — can exhibit a strictly positive quantum capacity when used in tandem.
In this talk, we investigate this phenomenon in the finite blocklength regime, where only of a finite number of channel uses, say n, is available. The goal is to determine the number of channel uses required to observe this phenomenon in practice. By leveraging the Choi representation of quantum channels and semidefinite programming techniques, we derive lower bounds on the n-shot quantum capacity of two known zero-capacity channels and compare them with known analytical bounds. These numerical results suggest that only a small number of channel uses may suffice to achieve superactivation in practice.
