We propose a secure and scalable file-encryption scheme for cloud systems by integrating Post-Quantum Cryptography (PQC), Quantum Key Distribution (QKD), and Advanced Encryption Standard (AES) within a distributed architecture. While prior studies have primarily focused on secure key exchange or authentication protocols (e.g., layered PQC-QKD key distribution), our scheme extends beyond key management by implementing a distributed encryption architecture that protects large-scale files through integrated PQC, QKD, and AES. To support high-throughput encryption, our proposed scheme partitions the target file into fixed-size subsets and distributes them across slave nodes, each performing parallel AES encryption using a locally reconstructed key from a PQC ciphertext. Each slave node receives a PQC ciphertext that encapsulates the AES key, along with a PQC secret key masked using QKD based on the BB84 protocol, both of which are centrally generated and managed by the master node for secure coordination. In addition, an encryption and transmission pipeline is designed to overlap I/O, encryption, and communication, thereby reducing idle time and improving resource utilization. The master node performs centralized decryption by collecting encrypted subsets, recovering the AES key, and executing decryption in parallel. Our evaluation using a real-world medical dataset shows that the proposed scheme achieves up to 2.37× speedup in end-to-end runtime and up to 8.11× speedup in encryption time over AES (Original). In addition to performance gains, our proposed scheme maintains low communication cost, stable CPU utilization across distributed nodes, and negligible overhead from quantum key management.