Pablo V. Parellada

Finite-size general security proofs for quantum key distribution based on Rényi 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 Rényi 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.

Finite-size general security proofs for QKD based on Rényi entropies offer 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 Rényi entropy, a difficult optimization problem that has commonly 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.

Computing key rates in QKD numerically is essential to unlock more powerful protocols, that uses more sophisticated measurement bases or quantum systems of higher dimension. It is a difficult optimization problem, that depends on minimizing a convex non-linear function, the relative entropy. The gold standard for solving such problems is a primal-dual interior-point algorithm, that is highly efficient and inherently gives upper and lower bounds. Recently one such algorithm was discovered for non-symmetric cones, a category that includes the relative entropy, and was previously out of reach.