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Quantum Foundations
Axiomatising the dagger category of complex Hilbert spaces
arXiv
Authors: Jan Paseka, Thomas Vetterlein
Year
2025
Paper ID
16932
Status
Preprint
Abstract Read
~2 min
Abstract Words
75
Citations
N/A
Abstract
We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of objecs, two further ones deal with the decomposition of objects, and a final axiom expresses a symmetry property. The categorical reconstruction of complex Hilbert spaces addresses foundational issues in quantum physics. We present a simplified alternative to recent characterisations.
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- This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
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- We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions.
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