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


author list (cited authors)

  • Nha, H., & Kim, J.

citation count

  • 63

complete list of authors

  • Nha, Hyunchul||Kim, Jaewan

publication date

  • July 2006