A computer scientist's reconstruction of quantum theory

Abstract

The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure of quantum systems comes from. From a computer scientist's perspective we would like to study quantum theory in a way that allows interesting transformations and compositions of systems and that also includes infinite-dimensional datatypes. Here we present such a compositional reconstruction of quantum theory that includes infinite-dimensional systems. This reconstruction is noteworthy for three reasons: it is only one of a few that includes no restrictions on the dimension of a system; it allows for both classical, quantum, and mixed systems; and it makes no a priori reference to the structure of the real (or complex) numbers. This last point is possible because we frame our results in the language of category theory, specifically the categorical framework of effectus theory.

42 pages

References in corpus (10)

• Characterizing quantum theory in terms of information-theoretic constraints
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• Terminality implies non-signalling
• Entanglement as an axiomatic foundation for statistical mechanics
• Categorical Operational Physics
• Effectuses in Categorical Quantum Foundations
• Sheaf representation of monoidal categories
• Axioms for the category of Hilbert spaces
• Quantum Theory from Principles, Quantum Software from Diagrams

Cited by in corpus (3)

• Symmetry-induced failures of tomographic locality: Constructing foil theories by twirling
• Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction
• A Categorical Construction of the Real Unit Interval