# A Categorical Reconstruction of Quantum Theory

arXiv: https://arxiv.org/abs/1804.02265 · HTML: https://mlsanity.com/paper/1804.02265/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Coinductive guide to inductive transformer heads](https://mlsanity.com/paper/2302.01834/) (2023)

## Abstract (arXiv)

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.