Operational Theories of Physics as Categories
arXiv:1602.06284
Abstract
We introduce a new approach to the study of operational theories of physics using category theory. We define a generalisation of the (causal) operational-probabilistic theories of Chiribella et al. and establish their correspondence with our new notion of an operational category. Our work is based on effectus theory, a recently developed area of categorical logic, to which we give an operational interpretation, demonstrating its relevance to the modelling of general probabilistic theories.
arXiv comment30 pages
References in corpus (9)
- Informational derivation of Quantum Theory
- Quantum Theory From Five Reasonable Axioms
- Probabilistic theories with purification
- A generalized no-broadcasting theorem
- Impossibility of deleting an unknown quantum state
- Reformulating and Reconstructing Quantum Theory
- Dilation of states and processes in operational-probabilistic theories
- Terminality implies non-signalling
- Quotient-Comprehension Chains
Cited by in corpus (9)
- Universal Properties in Quantum Theory
- Dagger and Dilation in the Category of Von Neumann algebras
- Categorical Operational Physics
- Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras
- A computer scientist's reconstruction of quantum theory
- Effectuses in Categorical Quantum Foundations
- Mathematical methods for resource-based type theories
- Morphisms in categories of nonlocal games
- Quantum channels as a categorical completion