Classification of all alternatives to the Born rule in terms of informational properties

Understand

The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding probabilities.

• In this work we keep the first group of postulates and characterize all alternatives to the second group that give rise to finite-dimensional sets of mixed states.
• We prove a correspondence between all these alternatives and a class of representations of the unitary group.
• Some features of these probabilistic theories are identical to quantum theory, but there are important differences in others.