Modal quantum theory (MQT) is a discrete model that is similar in structure to ordinary quantum theory, but based on a finite field instead of complex amplitudes. Its interpretation involves only the "modal" concepts of possibility and impossibility rather than quantitative probabilities. Despite its very simple structure, MQT nevertheless includes many of the key features of actual quantum physics, including entanglement and nonclassical computation. In this talk we describe MQT and explore how modal and probabilistic theories are related. Under what circumstances can we assign probabilities to a given modal structure?
