Abstract.
We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence classes under local unitary operations. For mixed states characterization of full tripartite entanglement is not yet solved in general; some partial results will be presented here.
Similar content being viewed by others
References
L. Gurvits, J. Comput. Syst. Sci. 69, 448 (2004)
A. Acín, A. Andrianov, L. Costa, E. Jané, J.I. Latorre, R. Tarrach, Phys. Rev. Lett. 85, 7 (2000)
A. Acín, A. Andrianov, E. Jané, R. Tarrach, J. Phys. A: Math. Gen. 34, 6725 (2001)
W. Dür, G. Vidal, J. Cirac, Phys. Rev. A 62, 062314 (2000)
L. Lamata, J. León, D. Salgado, E. Solano, Phys. Rev. A 74, 052336 (2006)
M. Plesch, V. Bužek, Phys. Rev. A 67, 012322 (2003)
M. Plesch, V. Bužek, Phys. Rev. A 68, 012313 (2003)
V. Coffman, J. Kundu, W.K. Wootters, Phys. Rev. A 61, 0532306 (2000)
C.S. Yu, H.S. Song, Phys. Lett. A 330, 377 (2004)
D. Meyer, N.R. Wallach, J. Math. Phys. 43, 4273 (2002)
G.K. Brennen, Quantum Inform. Comput. 3, 619 (2003)
F. Pan, D. Liu, G. Lu, J.P. Draayer, Int. J. Theor. Phys. 43, 1241 (2004)
P. Facchi, G. Florio, S. Pascazio, Phys. Rev. A 74, 042331 (2006)
R.F. Werner, Phys. Rev. A 40, 4277 (1989)
T. Radtke, S. Fritzsche, Comput. Phys. Commun. 175, 145 (2006)
J.J. Sakurai, Modern Quantum Mechanics (Addison-Wesley Publishing Company, 1994), pp. 183–184
W.K. Wootters, S. Hill, Phys. Rev. Lett. 78, 5022 (1997)
G. Vidal, R.F. Werner, Phys. Rev. A 65, 032314 (2002)
S. Barn, S.J.D. Phoenix, Phys. Rev. A 44, 535 (1991)
P. Rungta, V. Buzek, C.M. Caves, M. Hillery, G.J. Millburn, Phys. Rev. A 64, 042315 (2001)
R. Horodecki, M. Horodecki, P. Horodecki, K. Horodecki, arXiv: quant-ph/070225
P.Badziag, P. Deuar, M. Horodecki, P. Horodecki, R. Horodecki, J. Mod. Optics 49, 1289 (2002)
A. Miranowicz, A. Grudka, J. Opt. B: Quantum Semiclass. Opt. 6, 542 (2004)
A. Miranowicz, A. Grudka, Phys. Rev. A 70, 032326 (2004)
M.B. Plenio, S. Virmani, Quantum Inform. Comput. 7, 1 (2007)
M.B. Plenio, Phys. Rev. Lett. 95, 090503 (2005)
M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998)
P. Horodecki, Phys. Lett. A 232, 333 (1997)
A. Acín, D. Bruß, M. Lewnstein, A. Sanpera, Phys. Rev. Lett. 87, 040401 (2001)
D.Bruß et al., Phys. Rev. A 72, 014301 (2005)
W. Dür, J.I. Cirac, R. Tarrach, Phys. Rev. Lett. 83, 3562 (1999)
T. Eggeling, R.F. Werner, Phys. Rev. A 63, 042111 (2001)
W. Laskowki, M. Zukowski, Phys. Rev. A 72, 062112 (2005)
L.E. Ballentine, Quantum mechanics: a modern development (World Scientific Publishing, 1998)
G. Vidal, J. Mod. Optics 47, 355 (2000)
C.S. Yu, H.S. Song, Phys. Rev. A 73, 022325 (2006)
C.S. Yu, H.S. Song, Phys. Rev. A 73, 032322 (2006)
T.C. Wei, P.M. Goldbart, Phys. Rev. A 68, 024307 (2003)
R. Lohmayer, A. Osterloh, J. Siewert, A. Uhlmann, Phys. Rev. Lett. 97, 260502 (2006)
P.J. Love et al., Quantum Inf. Process. 6, 187 (2007)
S.J. Akhtarshenas, J. Phys. A 38, 6777 (2005)
H.A. Carteret, A. Higuchi, A. Sudbery, J. Math. Phys. 41, 7932 (2000)
C.S. Yu, H.S. Song, Phys. Rev. A 72, 022333 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sabín, C., García-Alcaine, G. A classification of entanglement in three-qubit systems. Eur. Phys. J. D 48, 435–442 (2008). https://doi.org/10.1140/epjd/e2008-00112-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2008-00112-5