Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Information and Computation

Distillability criterion for all bipartite Gaussian states

G. Giedke, L-M Duan, J. I. Cirac, P Zoller

Published Oct 1, 2001• 26 citations
Publisher

Abstract

We prove that all inseparable Gaussian states of two modes can be distilled into maximally entangled pure states by local operations. Using this result we show that a bipartite Gaussian state of arbitrarily many modes can be distilled if and only if its partial transpose is not positive.
DOI
10.26421/qic1.3-7

Related papers

Distillability Criterion for all bipartite Gaussian States

G. Giedke, Duan, L M, Zoller, P +1 more

We prove that all inseparable Gaussian states of two modes can be distilled into maximally entangled pure states by local operations. Using this result we show that a bipartite Gaussian state of arbitrarily many modes can be distilled if and only if its partial transpose is not positive.

•Apr 13, 2001•26 citations

Distillability Criterion for all Bipartite Gaussian States

G. Giedke, Luming Duan, J. I. Cirac +1 more

We prove that all inseparable Gaussian states of two modes can be distilled into maximally entangled pure states by local operations. Using this result we show that a bipartite Gaussian state of arbitrarily many modes can be distilled if and only if its partial transpose is not positive.

arXiv:quant-ph/0104072•Apr 13, 2001•0 citations

Entanglement Criteria for All Bipartite Gaussian States

G. Giedke, Barbara Kraus, Maciej Lewenstein +1 more

We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it allows us to find a pure product-state decomposition of any given separable Gaussian state. We also show that all bipartite Gaussian states with nonpositive partial transpose are distillable.

arXiv:quant-ph/0104050•Physical Review Letters•Oct 1, 2001•190 citations

Preparation of bipartite bound entangled Gaussian states in quantum optics

Shan Ma, Matthew J. Woolley, Xiaojun Jia +1 more

The positivity of the partial transpose is in general only a necessary condition for separability. There exist quantum states that are not separable, but nevertheless are positive under the partial transpose. States of this type are known as bound entangled states, meaning that these states are entangled but they do not allow distillation of pure entanglement by means of local operations and classical communication. We present a parametrization of a class of $2\ifmmode\times\else\texttimes\fi{}2$ bound entangled Gaussian states for bipartite continuous-variable quantum systems with two modes on each side. We propose an experimental protocol for preparing a particular bound entangled state in quantum optics. We then discuss the robustness properties of this protocol with respect to the occupation number of thermal inputs and the degrees of squeezing.

arXiv:1904.11748•Physical Review A•Aug 8, 2019•8 citations

All inseparable two-mode Gaussian continuous variable states are distillable

G. Giedke, L.-M. Duan, J. I. Cirac +1 more

We show that all entangled Gaussian states of two infinite dimensional systems can be distilled to maximally entangled states in finite dimensions. The distillation protocol involves local squeezing operations, local homodyne measurements with ancilla systems prepared in coherent states as well as local joint measurements of the total number operator of two copies of the state.

arXiv:quant-ph/0007061•Jul 18, 2000•2 citations

Gaussian Transformations and Distillation of Entangled Gaussian States

Jaromı́r Fiurášek

We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via local Gaussian operations and classical communication. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [preceding Letter, Phys. Rev. Lett. 89, 137903 ()]] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.

arXiv:quant-ph/0204069•Physical Review Letters•Sep 4, 2002•411 citations
The positivity of the partial transpose is in general only a necessary condition for separability. There exist quantum states that are not separable, but nevertheless are positive under the partial transpose. States of this type are known as bound entangled states, meaning that these states are entangled but they do not allow distillation of pure entanglement by means of local operations and classical communication. We present a parametrization of a class of $2\ifmmode\times\else\texttimes\fi{}2$ bound entangled Gaussian states for bipartite continuous-variable quantum systems with two modes on each side. We propose an experimental protocol for preparing a particular bound entangled state in quantum optics. We then discuss the robustness properties of this protocol with respect to the occupation number of thermal inputs and the degrees of squeezing.
We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via local Gaussian operations and classical communication. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [preceding Letter, Phys. Rev. Lett. 89, 137903 ()]] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.