Axioms for the category of Hilbert spaces and linear contractions

Abstract

The category of Hilbert spaces and linear contractions is characterised by elementary categorical properties that do not refer to probabilities, complex numbers, norm, continuity, convexity, or dimension.

17 pages; clarified proof of Lemma 20

References in corpus (3)

• With a Few Square Roots, Quantum Computing is as Easy as Π
• Sheaf representation of monoidal categories
• Universal Properties of Partial Quantum Maps

Cited by in corpus (2)

• Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
• Quantum Circuits Are Just a Phase