Quantum information geometric foundations: an overview


Kostecki, R. (2014). Quantum information geometric foundations: an overview. Perimeter Institute. https://pirsa.org/14110134


Kostecki, Ryszard. Quantum information geometric foundations: an overview. Perimeter Institute, Nov. 18, 2014, https://pirsa.org/14110134


          @misc{ pirsa_PIRSA:14110134,
            doi = {10.48660/14110134},
            url = {https://pirsa.org/14110134},
            author = {Kostecki, Ryszard},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantum information geometric foundations: an overview},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {nov},
            note = {PIRSA:14110134 see, \url{https://pirsa.org}}

Ryszard Kostecki University of Gdansk


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.