Few-Body Entanglement Manipulation

  • C. Spee
  • J. I. de Vicente
  • B. KrausEmail author
Part of the The Frontiers Collection book series (FRONTCOLL)


In order to cope with the fact that there exists no single maximally entangled state (up to local unitaries) in the multipartite setting, we introduced in [1] the maximally entangled set of n-partite quantum states. This set consists of the states that are most useful under conversion of pure states via Local Operations assisted by Classical Communication (LOCC). We will review our results here on the maximally entangled set of three- and generic four-qubit states. Moreover, we will discuss the preparation of arbitrary (pure or mixed) states via deterministic LOCC transformations. In particular, we will consider the deterministic preparation of arbitrary three-qubit (four-qubit) states via LOCC using as a resource a six-qubit (23-qubit) state respectively.


  1. 1.
    J.I. de Vicente, C. Spee, B. Kraus, Phys. Rev. Lett. 111, 110502 (2013)CrossRefGoogle Scholar
  2. 2.
    J.S. Bell, Physics 1, 195 (1964)Google Scholar
  3. 3.
    See e. g. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)Google Scholar
  4. 4.
    R. Horodecki et al., Rev. Mod. Phys. 81, 865 (2009)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    M. Hillery, V. Buẑek, A. Berthiaume, Phys. Rev. A 59, 1829 (1999). R. Cleve, D. Gottesman, H.-K. Lo, Phys. Rev. Lett. 83, 648 (1999)Google Scholar
  8. 8.
    R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    R.M. Gingrich, Phys. Rev. A 65, 052302 (2002)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    H.-K. Lo, S. Popescu, Phys. Rev. A 63, 022301 (2001)ADSCrossRefGoogle Scholar
  11. 11.
    M.A. Nielsen, Phys. Rev. Lett. 83, 436 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    E. Chitambar, Phys. Rev. Lett. 107, 190502 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    E. Chitambar, D. Leung, L. Mancinska, M. Ozols, A. Winter, Commun. Math. Phys. 328(1), 303–326 (2014). and references thereinGoogle Scholar
  14. 14.
    S. Turgut, Y. Gül, N.K. Pak, Phys. Rev. A 81, 012317 (2010). S. Kintas, S. Turgut, J. Math. Phys. 51, 092202 (2010)Google Scholar
  15. 15.
    B. Kraus, Phys. Rev. Lett. 104, 020504 (2010). Phys. Rev. A 82, 032121 (2010)Google Scholar
  16. 16.
    W. Dür, G. Vidal, J.I. Cirac, Phys. Rev. A 62, 062314 (2000)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    F. Verstraete, J. Dehaene, B. De Moor, H. Verschelde, Phys. Rev. A 65, 052112 (2002)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    D. M. Greenberger, M. Horne, A. Zeilinger, Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, ed. by M. Kafatos (Kluwer, Dordrecht, 1989), p.69Google Scholar
  19. 19.
    S. Ishizaka, M.B. Plenio, Phys. Rev. A 71, 052303 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    G. Gour, N.R. Wallach, New J. Phys. 13, 073013 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    C.H. Bennett, D.P. DiVincenzo, C.A. Fuchs, T. Mor, E. Rains, P.W. Shor, J.A. Smolin, W.K. Wootters, Phys. Rev. A 59, 1070 (1999)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    E. Chitambar, R. Duan, Phys. Rev. Lett. 103, 110502 (2009)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    G. Gour, N.R. Wallach, J. Math. Phys. 51, 112201 (2010)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    P. Facchi, G. Florio, G. Parisi, S. Pascazio, Phys. Rev. A 77, 060304(R) (2008)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    A. Acin, A. Andrianov, L. Costa, E. Jané, J.I. Latorre, R. Tarrach, Phys. Rev. Lett. 85, 1560 (2000)ADSCrossRefGoogle Scholar
  26. 26.
    J.I. de Vicente, T. Carle, C. Streitberger, B. Kraus, Phys. Rev. Lett. 108, 060501 (2012)CrossRefGoogle Scholar
  27. 27.
    C. Spee, J.I. de Vicente, B. Kraus, Phys. Rev. A 88, 010305(R) (2013)ADSCrossRefGoogle Scholar
  28. 28.
    C. Spee, J.I. de Vicente, B. Kraus, J. Math. Phys. 57, 052201 (2016)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Institute for Theoretical Physics, University of InnsbruckInnsbruckAustria
  2. 2.Departamento de MatemáticasUniversidad Carlos III de MadridMadridSpain

Personalised recommendations