Ensuring secure and efficient data processing in mobile edge computing (MEC) systems is a critical challenge. While quantum key distribution (QKD) offers unconditionally secure key exchange and homomorphic encryption (HE) enables privacy-preserving data processing, existing research fails to address the comprehensive trade-offs among QKD utility, HE security, and system costs. This paper proposes a novel framework integrating QKD, transciphering, and HE for secure and efficient MEC. QKD distributes symmetric keys, transciphering bridges symmetric encryption, and HE processes encrypted data at the server. We formulate an optimization problem balancing QKD utility, HE security, processing and wireless transmission costs. However, the formulated optimization is non-convex and NPhard. To solve it efficiently, we propose the Quantum-enhanced Homomorphic Encryption resource allocation (QuHE) algorithm. Theoretical analysis proves the proposed QuHE algorithm's convergence and optimality, and simulations demonstrate its effectiveness across multiple performance metrics.