Quantum Resource Theories and the Structure Induced by Majorization Preorder

BELLOMO, GUIDO

Workshop; Q-Turn; 2018

We present some results and discussions regarding the implications of the theory of majorization into the realm of quantum information. Majorization provides a way to preorder a set of finite dimensional real vectors and, as such, arises naturally when one deals with the states of finite dimensional quantum systems. In those cases, majorization induces a particular distance that brings a geometric view. However, most of those problems are usually attacked by using some other measures of distinguishability between quantum states. We show that in some cases this strategy hides the undesirable inconsistency between the majorization relation and the hierarchy induced by the alternative measures. We argue that in those problems majorization settles the most fundamental structure between quantum states, and we draw attention to the importance of study them from a perspective that privileges this structure. We partially illustrate these ideas showing some implications in the resource theory of quantum entanglement.