Entanglement criteria via the uncertainty relations in su(2) and su(1,1) algebras: Detection of non-Gaussian entangled states Academic Article uri icon


  • We derive a class of inequalities, from the uncertainty relations of the su(1,1) and the su(2) algebra in conjunction with partial transposition, that must be satisfied by any separable two-mode states. These inequalities are presented in terms of the su(2) operators Jx = (a† b+a b†) 2, Jy = (a† b-a b†) 2i, and the total photon number Na + Nb. They include as special cases the inequality derived by Hillery and Zubairy [Phys. Rev. Lett. 96, 050503 (2006)], and the one by Agarwal and Biswas [New J. Phys. 7, 211 (2005)]. In particular, optimization over the whole inequalities leads to the criterion obtained by Agarwal and Biswas. We show that this optimal criterion can detect entanglement for a broad class of non-Gaussian entangled states, i.e., the su(2) minimum-uncertainty states. Experimental schemes to test the optimal criterion are also discussed, especially the one using linear optical devices and photodetectors. © 2006 The American Physical Society.

published proceedings

  • Physical Review A

author list (cited authors)

  • Nha, H., & Kim, J

citation count

  • 61

complete list of authors

  • Nha, Hyunchul||Kim, Jaewan

publication date

  • July 2006