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We derive a class of inequalities, from the uncertainty relations of theSU(1,1) and the SU(2) algebra in conjunction with partial transposition, thatmust be satisfied by any separable two-mode states. These inequalities arepresented in terms of the su(2) operators J_x, J_y, and the total photon numberN_a+N_b. They include as special cases the inequality derived by Hillery andZubairy [Phys. Rev. Lett. 96, 050503 (2006)], and the one by Agarwal and Biswas[New J. Phys. 7, 211 (2005)]. In particular, optimization over the wholeinequalities leads to the criterion obtained by Agarwal and Biswas. We showthat this optimal criterion can detect entanglement for a broad class ofnon-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.Comment: published version, presentation polished with references added, 7  pages, 4 figure

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