General Probabilistic Theories with a Gleason-type Theorem

General probabilistic theories are shown to admit a Gleason-type theorem if and only if they satisfy the no-restriction hypothesis, or a “noisy” version of the hypothesis. Therefore, in precisely these theories we recover the state space by assuming that (i) states consistently assign probabilities to measurement outcomes and (ii) there is a unique state for every such assignment.

Link to the paper: https://arxiv.org/abs/2005.14166