Joint Optimization of Photon Source Deployment and Key Rate Allocation with Trusted Relay Path Identification in Qkd Networks

Quantum key distribution (QKD) is currently the only visible technology for secure symmetric key exchange between communicating parties. However, existing quantum photon sources (PSs) in QKD networks for generating keys between nodes are costly but offer limited achievable key rates. Moreover, achievable key rates across links diminish drastically with link distance, underscoring the importance of effectively identifying relay paths and strategically allocating PS resources. To optimize network costs, it is essential to jointly deploy PSs, allocate key rates across links, and determine relay paths based on anticipated traffic. To this end, we formulate a novel optimization problem, termed DAP, which simultaneously considers PS placement, key rate allocation, and relay path identification. Our proposed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(\log\vert V\vert)$</tex> approximation algorithm, ADAP, leverages an advanced linear programming (LP) conversion with tailored rounding techniques. Simulation results manifest that ADAP achieves at least an 83 % reduction in the number of PSs.