Finite-size quantum key distribution rates from R\'enyi entropies using conic optimization

Finite-size general security proofs for quantum key distribution based on R\'enyi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations based on the von Neumann entropy. However, deploying them requires minimizing the conditional R\'enyi entropy, a difficult optimization problem that has hitherto been tackled using ad-hoc techniques based on the Frank-Wolfe algorithm, which are unstable and can only handle particular cases. In this work, we introduce a method based on non-symmetric conic optimization for solving this problem. Our technique is fast, reliable, and completely general. We illustrate its performance on several protocols, whose results represent an improvement over the state of the art.