Optimizing the Decoy-State BB84 QKD Protocol Parameters

TL;DR

This paper presents a rigorous optimization approach for the Decoy-State BB84 QKD protocol that improves key-rate performance by eliminating heuristic assumptions in parameter selection.

Contribution

It introduces a method using linear and non-linear programming to optimize protocol parameters without heuristic simplifications, achieving tighter security analysis and better performance.

Findings

Enhanced key-rate performance over traditional heuristic methods

Tighter security analysis due to comprehensive optimization

Optimization feasible with limited computational resources

Abstract

The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making an number of heuristic assumptions. For instance, the number of decoy states is restricted to only one or two, with one of the decoy intensities set to a fixed value, and vacuum states are ignored as they are assumed to contribute only marginally to the secure key-rate. These assumptions simplify the optimization problem and reduce the size of search space significantly. However, they also cause the security analysis to be non-tight, and thereby result in sub-optimal performance. In this work, we follow a more rigorous approach using both linear and non-linear programs describing the optimization problem. Our approach, focusing on the Decoy-State BB84 protocol, allows heuristic assumptions to be omitted, and therefore results in a tighter security analysis with better protocol parameters. We show an improved performance for the Decoy-State BB84 QKD protocol, demonstrating that the heuristic assumptions typically made are too restrictive. Moreover, our improved optimization frameworks shows that the complexity of the performance optimization problem can also be handled without making heuristic assumptions, even with limited computational resources available.