This paper presents a robust theoretical framework to integrate blockchain-based security and privacy mechanisms with quantum machine learning (QML) in the edge computing domain within 6G networks. The burgeoning deployment of edge devices necessitates secure, privacy-preserving, and trustworthy infrastructures to support collaborative QML tasks while upholding data confidentiality at the network periphery. Leveraging blockchain technology's decentralized and immutable ledger capabilities, this framework manages access control, ensures data provenance, and verifies integrity in edge computing environments. Furthermore, integrating quantum-resistant cryptographic primitives is explored to fortify defenses against potential threats from quantum adversaries. In addition to these considerations, the paper incorporates the theory of quantum probability within the framework, particularly in the context of the central limit theorem, to account for the probabilistic nature of quantum systems and its implications on statistical inference in QML tasks. Detailed latency analysis reveals that blockchain processing time increases with transaction complexity, quantum processing time grows more slowly, and 6G transmission time remains constant due to high bandwidth capabilities. Incorporating machine learning components such as data preprocessing and model inference times provides a comprehensive understanding of edge computing performance. Combining blockchain-based security and privacy measures with QML techniques like federated learning and differential privacy, the envisioned framework strives to establish a secure and trusted ecosystem for collaborative QML tasks at the network edge. This theoretical endeavor, enriched by quantum probability theory and detailed latency analysis, lays a solid groundwork for further research and development in this burgeoning interdisciplinary domain, promising advancements in edge computing applications' efficiency, reliability, and security within future wireless communication infrastructures.