This paper looks at how operator theory can be used as a strict mathematical framework for processing quantum information. It discusses about how Hilbert spaces, spectral theory, and operator algebras can be used to describe quantum systems. The study also looks at Kraus decomposition and Stinespring dilation to talk about quantum channels and how they can be interpreted physically. In this study operator-theoretic method provide the huge data related to entanglement, decoherence, and channel stability by integrating the method as functional analysis with quantum physics.