Quantum key distribution rates from non-symmetric conic optimization

TL;DR

This paper introduces an efficient method for computing quantum key distribution rates by adapting a new optimization algorithm capable of handling the non-symmetric relative entropy cone, improving flexibility and performance.

Contribution

It adapts a recent non-symmetric cone optimization algorithm to quantum key rate calculations, enabling more efficient and flexible lower bound computations.

Findings

The new method outperforms previous techniques in speed and accuracy.

It handles the non-symmetric relative entropy cone effectively.

The approach simplifies the computation of key rates in complex QKD protocols.

Abstract

Computing key rates in quantum key distribution (QKD) numerically is essential to unlock more powerful protocols, that use 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 (quantum) relative entropy. Standard conic optimization techniques have for a long time been unable to handle the relative entropy cone, as it is a non-symmetric cone, and the standard algorithms can only handle symmetric ones. Recently, however, a practical algorithm has been discovered for optimizing over non-symmetric cones, including the relative entropy. Here we adapt this algorithm to the problem of computation of key rates, obtaining an efficient technique for lower bounding them. In comparison to previous techniques it has the advantages of flexibility, ease of use, and above all performance.