Incompatibility of effects in general probabilistic models

TL;DR

This paper establishes a precise criterion for when two effects in a general probabilistic model are incompatible, linking it to the minimal noise needed for compatibility.

Contribution

It provides a necessary and sufficient condition for effect incompatibility in models with convex state spaces, enhancing understanding of noise and compatibility.

Findings

Derived a condition for effect incompatibility

Connected incompatibility to minimal noise addition

Applicable to models with convex state spaces

Abstract

We give a necessary and sufficient condition for the incompatibility of a pair of effects in a general probabilistic model in which the state space is a total convex space, which can be obtained by minimising a real parameter. This has an interpretation in terms of the least noise that must be included to make the given pair compatible.