This paper introduces a novel post-quantum mutual authentication scheme for drones, leveraging Physical Unclonable Functions (PUFs) and cryptographic accumulators. By integrating PUFs, the scheme effectively mitigates drone cloning risks, while lattice-based cryptography ensures resilience against quantum computing attacks. The proposed approach enables secure, direct mutual authentication between drones without intermediaries. Cryptographic accumulators compress the entire drone identity database into a single element, significantly reducing storage demands on individual drones. The proposed scheme achieves superior communication efficiency compared to existing PUF-based post-quantum protocols for drones. Formal security verification using ProVerif confirms the robustness of the proposed scheme.