Structure of Quantum Theory

Representing quantum states by probability distributions comes at a price: a probability representation can keep track of which states are close to each other, or of how a system is composed of subsystems, but not of both (arXiv:2601.18872). This is an obstacle to reconstructing quantum theory from physical principles. Such a reconstruction requires a formalism for describing a landscape of possible theories. The most prominent is the framework of generalised probabilistic theories (GPTs). But in an arbitrary GPT, the only known way to make states explicit is through the probabilities of fiducial measurements, and so the price has to be paid. To remove the obstacle, we need a framework as general as GPTs that does not represent states by probabilities.

In this talk, I present a first step towards such a framework, which takes seriously the idea that states describe knowledge.