Tull, Sean - A Categorical Reconstruction of Quantum Theory

lmcs:5076 - Logical Methods in Computer Science, January 17, 2020, Volume 16, Issue 1 - https://doi.org/10.23638/LMCS-16(1:4)2020
A Categorical Reconstruction of Quantum Theory

Authors: Tull, Sean

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.

Volume: Volume 16, Issue 1
Published on: January 17, 2020
Submitted on: January 11, 2019
Keywords: Quantum Physics,Computer Science - Logic in Computer Science,Mathematics - Category Theory


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