Majorization in quantum mechanics

BOSYK, GUSTAVO MARTÍN

CABA

Workshop; International Workshop: Identity, indistinguishability and non-locality in quantum physic; 2017

Majorization is nowadays a well-established and powerful mathematical tool with many and different applications in several disciplines, such as economy, biology and physics, among others. The widespread applicability of majorization in the quantum realm is a consequence of the deep connections among majorization, partially ordered probability vectors, unitary matrices and the probabilistic structure of quantum mechanics. In this talk, I will review basic aspects of majorization, focusing on connections with some quantum information problems. In particular, I will present two different problems where majorization arises naturally. The first one consists in the role played by majorization as a disorder signature on quantum states, how quantum operations affect this, and which is the connection with other measures like entropies. The second problem consists in the study of entanglement transformations of bipartite pure states, applying local operations and classical communication.