# Incompatible measurements in a class of general probabilistic theories

## TL;DR

This paper explores measurement incompatibility in finite-dimensional general probabilistic theories, linking it to steering and nonlocality, and introduces tools to quantify and analyze incompatibility in various state spaces.

## Contribution

It introduces the concept of incompatibility witnesses, characterizes the maximum incompatibility degree in GPTs, and relates these findings to classical and quantum channels.

## Key findings

- Maximum incompatibility degree for quantum measurements identified
- Incompatibility is characterized by properties of affine maps into polysimplices
- Classical and quantum channels are closely related to polysimplices

## Abstract

We study incompatibility of measurements and its relation to steering and nonlocality in a class of finite dimensional general probabilistic theories (GPT).The basic idea is to represent finite collections of measurements as affine maps of a state space into a polysimplex and show that incompatibility is characterized by properties of these maps. We introduce the notion of an incompatibility witness and show its relation to incompatibility degree. We find the maximum incompatibility degree attainable by pairs of two-outcome quantum measurements and characterize state spaces for which incompatibility degree attains maximal values possible in GPT. As examples, we study the spaces of classical and quantum channels and show their close relation to polysimplices. This relation explains the super-quantum non-classical effects that were observed on these spaces.