INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
congresos y reuniones científicas
Majorization and entanglement transformations
BOSYK, GUSTAVO MARTÍN
Workshop; International Workshop on Applied Mathematics & Quantum Information; 2016
Università degli Studi di Cagliari
First, I will briefly introduce the concept of majorization between probability vectors and its main properties . In particular, I will present the majorization lattice obtained by Cicalese and Vaccaro . 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 |ψ> (initial state) and their goal is to transform it in another entangled pure-state |φ> (targetstate), by using only LOCC. A celebrated result of Nielsen gives the necessary and sufficient condition that makes possible this entanglement transformation process . Indeed, this process can be achieved if and only if the majorization relation ψ ≺ φ holds, where ψ and φ are probability vectors obtained by taking the squares of the Schmidt coefficients of the initial and target states, respectively. In general, this condition is not fulfilled. 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 fidelity between them . 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 .