Separability and distillability of bipartite Gaussian states -- the complete story
type: Item
instance of: scholarly article
zbMATH Open document ID: 1022.81004
author: Géza Giedke
author: Barbara Kraus
author: Peter Zoller
author: J. Ignacio Cirac
author: M. Lewenstein
author: Lu-Ming Duan
publication date: 2002-10-15T00:00:00Z
Mathematics Subject Classification ID: 81P15
Mathematics Subject Classification ID: 81P68
zbMATH DE Number: 1697684
zbMATH Keywords: quantum information theory
zbMATH Keywords: Gaussian states
zbMATH Keywords: separability conditions
zbMATH Keywords: distillability conditions
zbMATH Keywords: quantum entanglement
MaRDI profile type: Publication
OpenAlex ID: W2025879194
Wikidata QID: Q59458859
DOI: 10.1002/1521-3978(200110)49:10/11%3C973::AID-PROP973%3E3.0.CO;2-B
full work available at URL: https://doi.org/10.1002/1521-3978(200110)49:10/11%3C973::aid-prop973%3E3.0.co
title: Separability and distillability of bipartite Gaussian states -- the complete story
published in: Fortschritte der Physik
review text: Quantum information theory (QIT) is a new field of science where the processing of quantum information (QI) and communication play the important role. Here a notion of quantum entanglement (QET) keeps the crucial position. For a definition and description of QET one needs to understand a separability criterion of quantum states. Then for a processing of QET one needs to have pure entangled states. The process of getting such states from noisy entangled states is called a distillation. Let us stress here that in general for more than two entangled states both mentioned problems are unsolved yet. So every little step in this direction is of importance in building QIT, to be used, e.g., for quantum computing. NEWLINENEWLINENEWLINEThe problem of separability and distillability treated in this paper is solved for a special case of bipartite Gaussian states. By other words, necessary and sufficient conditions are formulated for two systems \(A\) and \(B\), composed of \(n\) and \(m\) modes respectively, in a Gaussian state, to be separable and distillable. Besides, it is shown that there are no so called bound entangled Gaussian states. So such states are distillable and thus useful for quantum communication.NEWLINENEWLINENEWLINEThe obtained result is important as Gaussian states are of particular interest, since most proposed applications in quantum communication are based on such states representing continuous variables case. Alas, for non-Gaussian states, however, both problems of separability and distillability remain open, representing two of great challenges of QIT.
reviewed by: Ladislav Andrey
description: scientific article; zbMATH DE number 1697684