Approximate transformations of bipartite pure-state entanglement from the majorization lattice

GUSTAVO BOSYK; GIUSEPPE SERGIOLI; HECTOR FREYTES; FEDERICO HOLIK; GUIDO BELLOMO

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2017

0378-4371

We study the problem of deterministic transformations of an initial pure entangled quantum state, j i, into a target pure entangled quantum state, jφi, by using local operations and classical communication (LOCC). A celebrated result of Nielsen [Phys. Rev. Lett. 83, 436 (1999)] gives the necessary and sucient condition that makes this entanglement transformation process possible. Indeed, this process can be achieved if and only if the majorization relation ≺ φ holds, where and φ are probability vectors obtained 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 [Phys. Rev. A 62, 012304 (2000)] have proposed a deterministic transformation using LOCC in order to obtain a target state jχopti most approximate to jφi in terms of maximal delity between them. Here, we show a strategy to deal with approximate entanglement transformations based on the properties of the majorization lattice. More precisely, we propose as approximate target state one whose Schmidt coecients are given by the supremum between and φ. Our proposal is inspired on the observation that delity does not respect the majorization relation in general. Remarkably enough, we nd that for some particular interesting cases, like two-qubit pure states or the entanglement concentration protocol, both proposals are coincident.