ON-LINE QLunch: Péter Vrana

Speaker: Péter Vrana, Budapest University of Technology and Economics

Title: Asymptotic relative submajorization 

Abstract:
Majorization and its generalizations have found important applications in information theory, quantum thermodynamics and more generally in resource theories. We study one such relation, an asymptotic variant of relative submajorization of pairs of quantum states. Our main tool is a recent generalization of Strassen's theorem on preordered semirings, which in our setting implies that the asymptotic preorder is characterized by real-valued monotone functions of pairs of states that are multiplicative under the tensor product and additive under the direct sum. We find this set of functions explicitly and prove a rate formula expressed in terms of sandwiched Rényi divergences. Based on

arXiv:2004.10587 and arXiv:2003.14176, joint work with Christopher Perry and Albert Werner.