Compatibility for Probabilistic Theories

Abstract

We define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT. We consider a PT called a concrete quantum logic that may have compatibility index strictly between 0 and 1, but we have not been able to show this yet. Finally, we show that observables in a PT can be represented by positive, vector-valued measures.

13 pages

References in corpus (2)

• Notes on Joint Measurability of Quantum Observables
• Comparing the degrees of incompatibility inherent in probabilistic physical theories

Cited by in corpus (7)

• An Invitation to Quantum Incompatibility
• Maximally incompatible quantum observables
• Joint measurability of quantum effects and the matrix diamond
• A necessary condition for incompatibility of observables in general probabilistic theories
• Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms
• A tensor norm approach to quantum compatibility
• Joint measurability through Naimark's theorem