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We present a first principles approach to a probabilistic description of nature based on two guiding principles: spacetime locality and operationalism. No notion of time or metric is assumed, neither any specific physical model. Remarkably, the emerging framework converges with the recently proposed positive formalism of quantum theory, obtained constructively from known quantum physics. However, it also seems to embrace classical physics.

I will present a new approach to information-theoretic foundations of quantum theory, that does not rely on probability theory, spectral theory, or Hilbert spaces. The direct nonlinear generalisations of quantum kinematics and dynamics are constructed using quantum information geometric structures over algebraic states of W*-algebras (quantum relative entropies and Poisson structure). In particular, unitary evolutions are generalised to nonlinear hamiltonian flows, while Lueders? rules are generalised to constrained relative entropy maximisations. Orthodox probability theory and quantum mechanics are special cases of this framework. I will also discuss the epistemic interpretation associated with this approach (rendering quantum theory as a framework for ontically noncommittal causal inference), as well as the possibility of deriving emergent space-times directly from quantum models.

Quantum information theory has taught us that quantum theory is just one possible probabilistic theory among many others. In the talk, I will argue that this "bird's-eye" perspective does not only allow us to derive the quantum formalism from simple physical principles, but also reveals surprising connections between the structures of spacetime and probability which can be phrased as mathematical theorems about information-theoretic scenarios.

Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behavior, yet that wave behavior disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitatively as an inequality, e.g., by Englert and Jaeger, Shimony, and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models (arXiv reference: 1403.4687).