Centre for Quantum Technologies, Singapore, kelvin.onggadinata@u.nus.edu
(joint work with Paweł Kurzyński and Dagomir Kaszlikowski)
A central problem in quantum foundations is to derive quantum theory from a simple and physically motivated principles. The standard formalism, one that is built upon the complex Hilbert space formalism, consists of axioms that are incredibly ad-hoc and unintuitive. A desire for a more intuitive set of postulates arises in the hope that a simple and minimal formulation is sufficient for the construction of quantum theories. In this work, we propose a simple information theoretic postulate where we look for a generalized dynamics in which certain Renyi entropies remain invariant for any given state. We find that the classical collision entropy is conserved under this and by demanding continuity of dynamical evolution, we can recover the full qubit system and its quantum dynamics. Therefore, constructing the basic elements of quantum theories without invoking Hilbert space at all.