Enhanced selection schedule for combined quantum key distribution protocol

Quantum Key Distribution (QKD) protocols involve a practical trade-off between key-generation throughput, hardware resources, and verification capability. Prepare-and-measure schemes such as BB84 are efficient for key generation, whereas entanglement-based schemes using Greenberger–Horne–Zeilinger (GHZ) states provide multipartite correlation checks but require more qubits and are more sensitive to current hardware noise. This work presents an implementation-oriented enhancement of a previously proposed GHZ–BB84 hybrid QKD architecture. Instead of using a fixed 50/50 protocol-selection schedule, we introduce an incrementally biased Ry-based selection circuit that increases the probability of selecting BB84 rounds after successful selection measurements while retaining a nonzero fraction of GHZ rounds for periodic correlation verification and key generation. We derive the selection probabilities for the accepted rounds and evaluate the resulting biased hybrid implementation using Qiskit and an IBM Quantum Device. In the 1000-state experiment, the enhanced combined protocol generated 477 final key bits, achieving ∼96.75% of the pure BB84 key count of 493 bits while retaining 10 GHZ-selected rounds out of 125 accepted rounds. Compared with the previous 50/50 hybrid baseline, the proposed selection schedule improves the final key-generation rate by 43.67%, increases qubit-use efficiency to 31.38%, and reduces the observed Quantum Bit Error Rate from ∼4% to about 1%. These results show that the biased selection schedule provides a practical rate–resource operating point for hybrid QKD implementations. The GHZ rounds are used for intermittent verification and key generation and are not assumed to transfer entanglement-based security guarantees to BB84 rounds; BB84-selected rounds retain the standard BB84 security requirements.