Abstract
We review the concepts of distillability and entanglement purification. We prove that all inseparable Gaussian two-mode continuous variable states are distillable. We present a entanglement purification protocol for Gaussian states and discuss a quantum optical implementation of this protocol.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, Nature 390, 575, (1997)
D. Boschi, S. Branca, F. De Martini, L. Hardy, S. Popescu, Phys. Rev. Lett. 80, 1121 (1998).
A. Ekert, Phys. Rev. Lett. 67, 661 (1991)
C.H. Bennett, G. Brassard, N. Mermin, Phys. Rev. Lett. 68, 557 (1992).
N. Gisin, Phys. Lett. A 210, 151 (1996)
C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J.A. Smolin, W.K. Wootters, Phys. Rev. Lett. 76, 722 (1996).
C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, Phys. Rev. A 54 3824 (1996).
C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996).
H.-J. Briegel, W. Dür, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 81, 5932 (1998).
M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
P. Horodecki, Phys. Lett. A 232, 233 (1997).
M. Lewenstein, D. Bruss, J.I. Cirac, B. Kraus, M. Kus, J. Samsonowicz, A. Sanpera, R. Tarrach, J. Mod. Opt. 47, 2481 (2000), quant-ph/006064.
P. Horodecki, M. Lewenstein Phys. Rev. Lett. 85, 2657 (2000).
W. Dür, J.I. Cirac, M. Lewenstein D. Bruß, Phys. Rev. A 61, 062313 (2000), quant-ph/9910022
D. DiVincenzo, P. Shor, J. Smolin, B. Terhal, A. Thapliyal, Phys. Rev. A 61, 062312 (2000), quant-ph/9910026.
M. Horodecki, P. Horodecki, Phys. Rev. A 59, 4206 (1999).
H.-A. Bachor, A guide to experiments in quantum optics, Wiley-VCH, Weinheim (1998).
L. Vaidman, Phys. Rev. A 49, 1473 (1994)
S.L. Braunstein, H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998).
A. Furusawa, J. Sørensen, S.L. Braunstein, C.A. Fuchs, H.J. Kimble, E.S. Polzik, Science 282, 706 (1998).
T.C. Ralph, Phys. Rev. A 61, 010303R (2000)
M. Hillery, Phys. Rev. A 61, 022309 (2000)
M. Reid, Phys. Rev. A 62, 062308 (2000), quant-ph/9909030
T.C. Ralph, Phys. Rev. A 62, 062307 (2000), quantph/0007024.
D. Petz, An Invitation to the Algebra of Canonical Commutation Relations, Leuven University Press, Leuven (1990).
C. Gardiner, P. Zoller, Quantum Noise 2nd ed., Springer-Verlag, Berlin (1999).
R.F. Werner, M.M. Wolf, Phys. Rev. Lett. 86, 3658 (2001), quantph/0009118(2000).
J. Manuceau, A. Verbeure, Comm. Math. Phys. 9, 293 (1968).
L. Duan, G. Giedke, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
R. Simon, Phys. Rev. Lett. 84, 2726 (2000).
G. Giedke, L.-M. Duan, J.I. Cirac, P. Zoller, Quant. Inf. Comp. 1(3), 79 (2001); quant-ph/0104072 and quant-ph/0007061.
C. Helstrom, Quantum detection and estimation theory, Associate Press, London (1976).
H. Scutaru, J. Math. Phys. 39, 6403 (1998).
H. Scutaru, Phys. Lett. A 141, 223 (1989).
S. Parker, S. Bose, M.B. Plenio, Phys. Rev A, 61, 032305 (1999).
G. Giedke, PhD Thesis, Universität Innsbruck (2001).
T. Opatrný, G. Kurizki, D.-G. Welsch, Phys. Rev. A 61, 032302 (1999).
L.-M. Duan, G. Giedke, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 84, 4002 (2000).
L.-M. Duan, G. Giedke, J.I. Cirac, P. Zoller, Phys. Rev. A 62, 032304 (2000).
A. S. Parkins, H. J. Kimble, Phys. Rev. A 61, 052104 (2000).
A. Imamoğlu, H. Schmid, G. Woods, M. Deutsch, Phys. Rev. Lett. 79, 1467 (1997); 81, 2836 (1998).
L.V. Hau, S.E. Harris, Z. Dutton, C.H. Behroozi, Nature 397, 594 (1999).
G. Giedke and J. I. Cirac, quant-ph/0204085.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Kluwer Academic Publishers
About this chapter
Cite this chapter
Giedke, G., Duan, LM., Cirac, J.I., Zoller, P. (2003). Distillability and Entanglement Purification for Gaussian States. In: Braunstein, S.L., Pati, A.K. (eds) Quantum Information with Continuous Variables. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1258-9_15
Download citation
DOI: https://doi.org/10.1007/978-94-015-1258-9_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6255-0
Online ISBN: 978-94-015-1258-9
eBook Packages: Springer Book Archive