A Categorical Reconstruction of Quantum Theory
2020
We reconstruct finite-dimensional quantum theory from categorical principles.
That is, we provide properties ensuring that a given physical theory described
by a dagger compact category in which one may `discard' objects is equivalent
to a generalised finite-dimensional quantum theory over a suitable ring $S$.
The principles used resemble those due to Chiribella, D'Ariano and Perinotti.
Unlike previous reconstructions, 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 theory
with $S$ being the complex numbers, or that over real Hilbert spaces with $S$
being the reals.
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