Journal of Mathematical Physics
Feedback | Help | Exit
Search:
   
 
 
 
Previous Article
The uniqueness theorem for entanglement measures
We explore and develop the mathematics of the theory of entanglement measures. After a careful review and analysis of definitions, of preliminary results, and of connections between conditions on enta...
Next Article
Entanglement and perfect quantum error correction
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure. ©2002 American Institute of Physics.

Global entanglement in multiparticle systems

J. Math. Phys. 43, 4273 (2002); doi:10.1063/1.1497700

Issue Date: September 2002

You are not logged in to this journal. Log in

David A. Meyer and Nolan R. Wallach
Project in Geometry and Physics, Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112
We define a polynomial measure of multiparticle entanglement which is scalable, i.e., which applies to any number of spin-(1/2) particles. By evaluating it for three particle states, for eigenstates of the one dimensional Heisenberg antiferromagnet and on quantum error correcting code subspaces, we illustrate the extent to which it quantifies global entanglement. We also apply it to track the evolution of entanglement during a quantum computation. ©2002 American Institute of Physics.
History: Received 23 January 2002; accepted 16 May 2002
Permalink: http://link.aip.org/link/?JMAPAQ/43/4273/1
BUY THIS ARTICLE   (US$24)
Download PDF (72 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 03.67.Lx
    Quantum mechanics, field theories, and special relativity Quantum information Quantum computation
  • 03.65.Ta
    Quantum mechanics, field theories, and special relativity Quantum mechanics Foundations of quantum mechanics; measurement theory
  • 03.65.Ge
    Quantum mechanics, field theories, and special relativity Quantum mechanics Solutions of wave equations: bound states
  • 02.30.Mv
    Mathematical methods in physics Function theory, analysis Approximations and expansions
  • YEAR: 2002

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (35)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. E. Schrödinger, Naturwissenschaften 23, 807 (1935);
  2. 23, 823 (1935);
  3. 23, 844 (1935).
  4. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
  5. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).
  6. G. Vidal, J. Mod. Opt. 47, 355 (2000).
  7. G. Vidal, Phys. Rev. Lett. 83, 1046 (1999).
  8. D. Bohm, Quantum Theory (Prentice-Hall, New York, 1951).
  9. D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer, Boston, 1989), p. 69.
  10. N. D. Mermin, Phys. Today 43, 9 (June 1990).
  11. N. Linden and S. Popescu, Fortschr. Phys. 46, 567 (1998).
  12. M. Grassl, M. Rötteler, and T. Beth, Phys. Rev. A 58, 1833 (1998).
  13. H. A. Carteret and A. Sudbery, J. Phys. A 33, 4981 (2000).
  14. A. Sudbery, J. Phys. A 34, 643 (2001).
  15. A. Acín, A. Andrianov, L. Costa, E. Jané, J. I. Latorre, and R. Tarrach, Phys. Rev. Lett. 85, 1560 (2000).
  16. A. Acín, A. Andrianov, E. Jané, and R. Tarrach, J. Phys. A 34, 6725 (2001).
  17. D. A. Meyer and N. R. Wallach, in Mathematics of Quantum Computation, edited by R. K. Brylinski and G. Chen (CRC, Boca Raton, 2002), p. 77.
  18. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A 61, 052306 (2000).
  19. D. A. Meyer and N. R. Wallach, in preparation.
  20. P. A. M. Dirac, Proc. R. Soc. London, Ser. A 112, 661 (1926).
  21. W. Heisenberg, Z. Phys. 49, 619 (1928).
  22. H. A. Bethe, Z. Phys. 71, 205 (1931).
  23. K. M. O'Connor and W. K. Wootters, Phys. Rev. A 63, 052302 (2001).
  24. D. Gottesman, "Stabilizer Codes and Quantum Error Correction," Ph.D. thesis, Caltech, physics, 1997;
    25. quant-ph/9705052.
  25. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
  26. R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, Phys. Rev. Lett. 77, 198 (1996).
  27. R. Cleve, D. Gottesman, and H.-K. Lo, Phys. Rev. Lett. 83, 648 (1999).
  28. P. W. Shor, Phys. Rev. A 52, R2493 (1995).
  29. M. H. Freedman and D. A. Meyer, Found. Comput. Math. 1, 325 (2001).
  30. H. Barnum and N. Linden, J. Phys. A 34, 6787 (2001).
  31. L. K. Grover, in Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, Philadelphia, PA, 22–24 May 1996 (ACM, New York, 1996), p. 212.
  32. A. Wong and N. Christensen, Phys. Rev. A 63, 044301 (2001).
  33. J. Eisert and H. J. Briegel, Phys. Rev. A 64, 022306 (2001).
  34. G. Vidal and R. F. Werner, Phys. Rev. A 65, 032314 (2002).
  35. J. Preskill, J. Mod. Opt. 47, 127 (2000).
  36. H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001).
  37. M. C. Arnesen, S. Bose, and V. Vedral, Phys. Rev. Lett. 87, 017901 (2001).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics