Mathematical Physics Seminar
One can associate a notion of quantum relative entropy to any convex function on the real line, in analogy with the relative entropy of a quasi-free state over a CAR or CCR algebra expressed in terms of its reduced one-body density matrix. We characterize the convex functions for which this relative entropy is monotone. Here, the notion of monotonicity relies on the decomposition of the underlying Hilbert space into a direct sum, rather than a decomposition into a tensor product as is usually done. This monotonicity property is used to properly define the relative entropy in infinite dimensions, and to derive Klein inequalities. This definition of the relative entropy is also used to study the time evolution of quantum systems around a translation-invariant stationary state. Joint work with Mathieu Lewin (CNRS/Paris-Dauphine).