XXXIII Workshop on Geometric Methods in Physics 29.06-5.07.2014

Ryszard Kostecki

Towards nonlinear quantum information geometric foundations of quantum theory

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 Banach Lie-Poisson structure). In particular, unitary evolution is 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 conceptual changes associated with this approach (a shift from quantum deductive logic to quantum inductive logic/bayesianity), as well as the possibility of deriving emergent space-times directly from quantum models.

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