  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 J_x, J_y, and the total photon number
N_a+N_b. 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.
