Towards Non-linear Quantum Information Foundations

          @misc{ pirsa_PIRSA:12010138,
            doi = {10.48660/12010138},
            url = {https://pirsa.org/12010138},
            author = {Kostecki, Ryszard},
            keywords = {Quantum Foundations, Quantum Fields and Strings},
            language = {en},
            title = {Towards Non-linear Quantum Information Foundations},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {jan},
            note = {PIRSA:12010138 see, \url{https://pirsa.org}}
          }
          

Abstract

I will present a new approach to information theoretic foundations of quantum theory, developed in order to encompass quantum field theory and curved space-times. Its kinematics is based on the geometry of spaces of integrals on W*-algebras, and is independent of probability theory and Hilbert spaces. It allows to recover ordinary quantum mechanical kinematics as well as emergent curved space-times. Unlike the approaches based on lattices of projections, this kinematics provides a direct mathematical generalisation of the ordinary probability theory to the regime of non-commutative algebras. The new quantum information dynamics is provided by the constrained maximisation of quantum relative entropy. The von Neumann-Lueders rule and several other rules of that type, including Bayes' rule in commutative case, are the special cases of it. Using Favretti's generalisation of the Jaynes-Mitchell source theory, I will show how this dynamics allows one to derive `interacting QFT'-like correlation functions and perturbation expansions in geometric terms of experimental control-and-response parameters, without using Hilbert spaces or measure spaces. Finally, I will present a new bayesian interpretation of quantum theory, aimed at dealing with the intersubjective experimental verifiability, but without providing any ontological claims. Quite noticeably, this interpretation leads to a concrete category theoretic formulation of the new foundations.