127
Views
0
CrossRef citations to date
0
Altmetric
Articles

Constructing k-Schmidt witnesses for infinite-dimensional systems

&
Pages 754-764 | Received 29 Oct 2013, Accepted 12 Feb 2014, Published online: 17 Apr 2014

References

  • Nielsen MA, Chuang IL. Quantum computation and quantum information. Cambridge: Cambridge University Press; 2000.
  • Horodecki M, Horodecki P, Horodecki R. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A. 1996;223:1–8.
  • Hou J, Qi X. Constructing entanglement witnesses for infinite-dimensional systems. Phys. Rev. A. 2010;81:062351.
  • Hou J. A characterization of positive linear maps and criteria of entanglement for quantum states. J. Phys. A Math. Theor. 2010;43:385201.
  • Qi X, Hou J. Detecting entanglement of states by entries of their density matrices. Int. J. Theor. Phys. 2012;51:2003–2014.
  • Shirokov ME. The Schmidt number and partially entanglement breaking channels in infinite dimensions. Math. Notes. 2013;93:766–779. arXiv:1110.4363.
  • Sperling J, Vogel W. Determination of the Schmidt number. Phys. Rev. A. 2011;83:042315.
  • Sperling J, Vogel W. The Schmidt number as a universal entanglement measure. Phys. Scr. 2011;83:045002.
  • Terhal BM, Horodecki P. Schmidt number for density matrices. Phys. Rev. A. 2000;61:040301.
  • Guo Y, Qi X, Hou J. Sufficient and necessary conditions of separability for bipartite pure states in infinite-dimensional systems. Chinese Sci. Bull. 2011;56:840–846.
  • Zhu S, Ma Z. Topologies on quantum states. Phys. Lett. A. 2010;374:1336–1341.
  • Bhatia R. Matrix analysis. Vol. 169, Graduate texts in mathematics. New York (NY): Springer; 1997.
  • Hou J. A characterization of positive elementary operators. J. Operator Theory. 1998;39:43–58.
  • Johnston N, Kribs DW. A family of norms with applications in quantum information theory. J. Math. Phys. 2010;51:082202.
  • Markus AS. The eigen- and singular values of the sum and product of linear operators. Russian Math. Surveys. 1964;19:91–120.
  • Perfect H. A theorem of Hardy, Littlewood and Polya and some related results for infinite vectors. Proc. Camb. Phil. Soc. 1967;63:1125–1134.
  • Dixon JD, Mortimer B. Permutation groups. Vol. 163, Texts in mathematics. New York (NY): Springer-Verlag; 1996.
  • Hou J, Li C-K, Poon Y-T, Qi X, Sze N-S. Criteria and new classes of k-positive maps. Forthcoming. arXiv:1211.0386.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.