Axiomatising the dagger category of complex Hilbert spaces

TL;DR

This paper provides a purely categorical axiomatization of the dagger category of complex Hilbert spaces, simplifying previous characterizations and addressing foundational issues in quantum physics.

Contribution

It introduces a new, more interpretable set of axioms for the dagger category of complex Hilbert spaces, avoiding complex algebraic conditions.

Findings

Axioms enable categorical reconstruction of complex Hilbert spaces

Simplifies previous characterizations of the dagger category

Addresses foundational issues in quantum physics

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.