A computer scientist's reconstruction of quantum theory
arXiv:2109.10707 · doi:10.1088/1751-8121/ac8459
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.
arXiv comment42 pages
References in corpus (39)
- Informational derivation of Quantum Theory
- Quantum Theory From Five Reasonable Axioms
- Characterizing quantum theory in terms of information-theoretic constraints
- A derivation of quantum theory from physical requirements
- Higher-order interference and single-system postulates characterizing quantum theory
- Quantum theory from questions
- Quantum Logic in Dagger Kernel Categories
- Thermodynamics and the structure of quantum theory
- Reconstructing quantum theory from diagrammatic postulates
- Completeness of dagger-categories and the complex numbers
- Categorical Probabilistic Theories
- Terminality implies non-signalling
- Composites and Categories of Euclidean Jordan Algebras
- Conditional probability, three-slit experiments, and the Jordan algebra structure of quantum mechanics
- Infinite-dimensional Categorical Quantum Mechanics
- Derivation of the Rules of Quantum Mechanics from Information-Theoretic Axioms
- An effect-theoretic reconstruction of quantum theory
- Space in Monoidal Categories
- Sequential Product Spaces are Jordan Algebras
- Entanglement as an axiomatic foundation for statistical mechanics
- Quantum Programming with Inductive Datatypes: Causality and Affine Type Theory
- Quotient-Comprehension Chains
- Poisson spaces with a transition probability
- The Category of Von Neumann Algebras
- Von Neumann Algebras form a Model for the Quantum Lambda Calculus
- Dagger and Dilation in the Category of Von Neumann algebras
- Operational Theories of Physics as Categories
- Orthomodular lattices, Foulis Semigroups and Dagger Kernel Categories
- Categorical Operational Physics
- A Categorical Reconstruction of Quantum Theory
- Commutativity in Jordan Operator Algebras
- A simple and quantum-mechanically motivated characterization of the formally real Jordan algebras
- Total and Partial Computation in Categorical Quantum Foundations
- Three characterisations of the sequential product
- The three types of normal sequential effect algebras
- Sheaf representation of monoidal categories
- Effectuses in Categorical Quantum Foundations
- Axioms for the category of Hilbert spaces
- Quantum Theory from Principles, Quantum Software from Diagrams