Quantum operators: A classical perspective

We review current research in the field of categorical quantum mechanics. We place the category of relations within the same categorical framework and point out the similarities with the category of Hilbert spaces. Subsequently, we provide a categorical model for investigating the spectral theorem (as provided in [22]), within the context of an internally diagonalisable element and apply these ideas to both categories mentioned. We find out that while all normal operators can be internally diagonalisable in the category of Hilbert spaces – this is not the case for the category of Relations. We conclude by providing insights on how we can separate the internally diagonalisable elements within the set of normal operators .