Speaker: Esko Keski-Vakkuri
Title:"Majorization and applications to quantum information"

Majorization was defined by Hardy, Littlewood and Pólya as a partial order, first for probability vectors. Later, generalizations were constructed
for probability densities and measurable functions. The discrete definition can be applied to density operators using their eigenvalues to define probability vectors.
For a pair of states with a majorization relation, there is an infinite class of monotones: quantities which are either non-decreasing or non-increasing. 
For example, the von Neumann entropy is monotonic under majorization. Furthermore, majorization between input and output states is an automatic result
from large classes of quantum operations (due to theorems by Nielsen and by Uhlmann).  These theorems thus provide a "first-principles" understanding
for changes in entropy in certain cases. More generally, majorization has an important role in so-called resource theories.