Department of Physics • University of Cologne

The postulates of quantum mechanics can be divided into two parts: the dynamical part which defines the pure states, their dynamics and composition rule and the probabilistic part which defines the structure of measurements and the probability rule. In this talk I will show that the dynamical part of quantum theory fully determines the probabilistic part, within the operational framework. First I will show that for single systems there are infinitely many probabilistic structures compatible with the dynamical structure, and that these can be put into correspondence with certain representations of the unitary group. Following this I will outline the operational conditions which arise when considering multiple systems, and how they constrain the possible probabilistic structures. I will then outline how the condition of associativity (of systems) singles out the measurement postulates of quantum mechanics amongst all possible alternatives. In a final part I will discuss how this result relates to existing work, such as Gleason’s theorem and Zurek’s derivation of the Born rule from envariance.