Transition probabilities of normal states determine the Jordan structure of a quantum system
Transition probabilities of normal states determine the Jordan structure of a quantum system
Let $\Phi:\mathfrak{S}(M_1)\to \mathfrak{S}(M_2)$ be a bijection (not assumed affine nor continuous) between the sets of normal states of two quantum systems, modelled on the self-adjoint parts of von Neumann algebras $M_1$ and $M_2$, respectively. This paper concerns with the situation when $\Phi$ preserves (or partially preserves) one of the following …