QKD security proofs for decoy-state BB84: protocol variations, proof techniques, gaps and limitations

Abstract: We review the current status of security proofs for practical decoy-state Quantum Key Distribution using the BB84 protocol, focusing on optical implementations with weak coherent pulses and threshold photodetectors. The primary aim of this review is to highlight gaps in the existing literature. Such gaps may arise, for instance, from mismatches between detailed protocol specifications and proof technique elements, reliance on earlier results based on different assumptions, or protocol choices that overlook real world requirements. While substantial progress has been made, our overview draws attention to the details that still demand careful attention.