Abstract.
We construct an explicit model where it can be established if a two mode pure Gaussian system is entangled or not by acting only on one of the parts that constitute the system. Measuring the dispersion in momentum and the time evolution of the dispersion in position of one particle we can tell if entanglement is present as well as the degree of entanglement of the system.
Similar content being viewed by others
References
E. Schrödinger, Proc. Camb. Phil. Soc. 31, 555 (1935)
A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935)
J.S. Bell, Physics 1, 195 (1964)
C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)
C.H. Bennett, G. Brassard, N.D. Mermin, Phys. Rev. Lett. 68, 557 (1992)
A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991)
A. Peres, Phys. Rev. Lett. 77, 1413 (1996)
M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)
R. Simon, Phys. Rev. Lett. 84, 2726 (2000)
L-M. Duan, G. Giedke, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 84, 2722 (2000)
To recover the Simon separability criterion as it was presented in Simon's paper simon we should substitute ħ2 in equation (20) by ħ2/4. This difference is due to the fact that Simon's CM is defined as the half of our CM γ. We use the same notation as duan
C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)
C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J.A. Smolin, W.K. Wootters, Phys. Rev. Lett. 76, 722 (1996)
V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997)
V. Vedral, M.B. Plenio, K. Jacobs, P.L. Knight, Phys. Rev. A 56, 4452 (1997)
U. Leonhardt, M.G. Raymer, Phys. Rev. Lett. 76, 1985 (1996)
T. Richter, A. Wünsche, Phys. Rev. A 53, R1974 (1996)
Ch. Kurtsiefer, T. Pfau, J. Mlynek, Nature 386, 150 (1997)
C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (Hermann and John Wiley & Sons, Paris, 1977), Vol. 2, Chap. 1, Complement GI
G. Arfken, Mathematical Methods for Physicists (Academic Press, Orlando, 1985), Chap. 8
B.-G. Englert, K. Wódkiewicz, Phys. Rev. A 65, 054303 (2002)
G. Giedke, M.M. Wolf, O. Krüger, R.F. Werner, J.I. Cirac, Phys. Rev. Lett. 91, 107901 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rigolin, G., Escobar, C. Local detection of entanglement. Eur. Phys. J. D 37, 291–296 (2006). https://doi.org/10.1140/epjd/e2005-00301-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2005-00301-8