Incompatible measurements in a class of general probabilistic theories

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.

Title changed, presentation improved. 18 pages in RevTex, 2 figures, comments welcome

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Cited by in corpus (28)

• Quantum Incompatibility Witnesses
• General probabilistic theories: An introduction
• Incompatibility robustness of quantum measurements: a unified framework
• Quantum random access codes and incompatibility of measurements
• Entanglement and superposition are equivalent concepts in any physical theory
• Witnessing incompatibility of quantum channels
• Jordan products of quantum channels and their compatibility
• Universal gaps for XOR games from estimates on tensor norm ratios
• Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms
• Compatibility of quantum measurements and inclusion constants for the matrix jewel
• Incompatibility in restricted operational theories: connecting contextuality and steering
• Compact convex structure of measurements and its applications to simulability, incompatibility, and convex resource theory of continuous-outcome measurements
• The compatibility dimension of quantum measurements
• Assemblages and steering in general probabilistic theories
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Testing incompatibility of quantum devices with few states
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
• A tensor norm approach to quantum compatibility
• Maximal violation of steering inequalities and the matrix cube
• Entropic Uncertainty Relations in a Class of Generalized Probabilistic Theories
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification
• Structure of quantum and classical implementations of Popescu-Rohrlich box
• Incompatibility of effects in general probabilistic models
• Symmetries and Wigner representations of operational theories
• Comparing quantum incompatibility of device sets from an operational perspective
• One-shot and asymptotic classical capacity in general physical theories
• Polytope compatibility -- from quantum measurements to magic squares
• Information transfer in generalized probabilistic theories based on weak repeatability