Quantum theory from categorical principles

A Categorical Reconstruction of Quantum Theory

We provide properties ensuring that a given physical theory describedby a dagger compact category in which one may `discard'objects is equivalentto a generalised finite-dimensional quantum theory over a suitable ring.Our axioms and proof are fully categorical in nature, in particular not requiring tomography assumptions.Specialising the result to probabilistic theories we obtain either traditional quantum theorywith being the complex numbers, or that over real hilbert spaces with being the reals.