In transportation cyber-physical systems (CPS), ensuring safety and reliability in real-time decision-making is essential for successfully deploying autonomous vehicles and intelligent transportation networks. However, these systems face significant challenges, such as computational complexity and the ability to handle ambiguous inputs like shadows in complex environments. This paper introduces a Quantum Deep Convolutional Neural Network (QDCNN) designed to enhance the safety and reliability of CPS in transportation by leveraging quantum algorithms. At the core of QDCNN is the UU† method, which is utilized to improve shadow detection through a propagation algorithm that trains the centroid value with preprocessing and postprocessing operations to classify shadow regions in images accurately. The proposed QDCNN is evaluated on three datasets on normal conditions and one road affected by rain to test its robustness. It outperforms existing methods in terms of computational efficiency, achieving a shadow detection time of just 0.0049352 seconds, faster than classical algorithms like intensity-based thresholding (0.03 seconds), chromaticity-based shadow detection (1.47 seconds), and local binary pattern techniques (2.05 seconds). This remarkable speed, superior accuracy, and noise resilience demonstrate the key factors for safe navigation in autonomous transportation in real-time. This research demonstrates the potential of quantum-enhanced models in addressing critical limitations of classical methods, contributing to more dependable and robust autonomous transportation systems within the CPS framework.