Luxquanta, ICFO and the University of Valladolid researchers have dramatically accelerated a critical calculation within quantum key distribution, reducing processing times from tens of seconds to a fraction of a second without compromising security. The team reformulated the computation of Rényi entropy, a measure of uncertainty for potential eavesdroppers, as a conic optimization problem, creating a more efficient and reliable method, Luxquanta says.

“Forty years ago, not even Bennett and Brassard could have guessed how quantum cryptography would look today,” says Dr. Carlos Pascual-García, Head of Quantum Theory at Luxquanta, highlighting the rapid evolution of the field and enabling faster, more scalable quantum-safe communication.

Rényi Entropy Reformulation Enables Faster QKD Calculations

This speed improvement stems from recasting the complex calculation as a conic optimization problem, allowing for a more direct and efficient solution. Instead of approximating the entropy function incrementally, the team constructed a mathematical cone mirroring its geometry, ensuring precision even in challenging scenarios where older methods faltered. The core of this advancement lies in Rényi entropy, a concept originating in information theory and now central to determining the secure key rate in QKD systems.

This measure quantifies the uncertainty remaining for a potential eavesdropper after accounting for all observed data, effectively defining the boundaries of secure communication. By precisely calculating Rényi entropy, the team has not only accelerated the process but also enhanced its numerical reliability, a critical factor for real-world implementation. “Moreover, our method is not only faster, but also more systematic and numerically precise than previous approaches,” explained Mariana Navarro, first author of the published study.

Beyond simply speeding up existing protocols, this new approach unlocks the ability to explore more complex QKD designs and analyze system limitations with greater ease. Researchers can now efficiently quantify the impact of factors like signal loss or detector imperfections on key generation rates, and accurately determine the maximum distance between communicating parties while maintaining provable security.

“At first, we were amazed by the speed of our strategy,” recalls Mariana Navarro, highlighting the unexpected efficiency gained through their mathematical reformulation. The team is already building on this work, pursuing broader goals with preliminary results appearing promising.

At first, we were amazed by the speed of our strategy.
Mariana Navarro, first author of the article

LuxQuanta Advances Security Bounds for Practical QKD Protocols

This speed improvement directly addresses a bottleneck in verifying the security of QKD systems, enabling more rapid assessment of potential vulnerabilities. The team’s method allows for reliable convergence even in protocols historically difficult to certify, such as continuous-variable QKD using a limited number of coherent states, where older solvers often failed, according to Luxquanta.

While Rényi entropies offer more precise security bounds than older methods, their computational complexity has long been a barrier to widespread adoption. This newfound computational efficiency unlocks the ability to rigorously analyze factors that degrade key rates, including signal loss and imperfections in detectors.

Researchers can now efficiently compare different protocol designs on a level playing field, determining which configurations offer the strongest security for a given set of constraints. The team is already extending the approach toward more complex QKD implementations like decoy-state BB84 and measurement-device-independent QKD. The team’s work, published in PRX Quantum, was supported by funding from the Government of Spain and the European Union’s Horizon Europe program.