Distances between States and between Predicates

Abstract

This paper gives a systematic account of various metrics on probability distributions (states) and on predicates. These metrics are described in a uniform manner using the validity relation between states and predicates. The standard adjunction between convex sets (of states) and effect modules (of predicates) is restricted to convex complete metric spaces and directed complete effect modules. This adjunction is used in two state-and-effect triangles, for classical (discrete) probability and for quantum probability.

References in corpus (4)

• Quantum Computing
• Bialgebraic Semantics for Logic Programming
• A Recipe for State-and-Effect Triangles
• The Category of Von Neumann Algebras

Cited by in corpus (6)

• Sequential Product Spaces are Jordan Algebras
• The Category of Von Neumann Algebras
• Dagger and Dilation in the Category of Von Neumann algebras
• Three characterisations of the sequential product
• Effectuses in Categorical Quantum Foundations
• Drawing with Distance