Majorization and entanglement transformations

BOSYK, GUSTAVO MARTÍN

La Plata

Jornada; VI Jornadas de Fundamentos de Cuántica: el problema del observador; 2016

First, I will briefly introduce the concept of majorization between probability vectors and its main properties [1]. In particular, I will present the majorization lattice obtained by Cicalese and Vaccaro [2]. Then, I will address the problem of entanglement transformations by using local operations and classical communications (LOCC). More precisely, the problem consists in two parties, Alice and Bob, that share an entangled pure-state psi (initial state) and their goal is to transform it in another entangled pure-state phi (target state), by using only LOCC. A celebrated result of Nielsen gives the necessary and sufficient condition that makes possible this entanglement transformation process [3]. Indeed, this process can be achieved if and only if a majorization relation between psi and phi holds, where psi and phiare probability vectorsobtained by taking the squares of the Schmidt coecients of the initial and target states, respectively. In general, this condition is not fullled. However, one can look for an approximate entanglement transformation. Vidal et. al have proposed a deterministic transformation using LOCC in order to obtain a state most approximate to target in terms of maximal delity between them [4]. In this talk, I will present an alternative proposal by exploiting the fact that majorization is indeed a lattice for the set of probability vectors [5].