All measurements in a probabilistic theory are compatible if and only if the state space is a simplex

Abstract

We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome measurements to be compatible and we use these conditions to show that there exist incompatible measurements whenever the state space is not a simplex. We also formulate the linear programming problem for the compatibility of two-outcome measurements.

References in corpus (3)

• A generalized no-broadcasting theorem
• Joint measurability of generalized measurements implies classicality
• Blocks of homogeneous effect algebras

Cited by in corpus (5)

• Incompatibility of quantum channels
• A necessary condition for incompatibility of observables in general probabilistic theories
• Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality
• Strongly symmetric spectral convex bodies are Jordan algebra state spaces
• Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories