We derive a class of inequality relations, using both the sum uncertainty relations of su(2) algebra operators and the Schrodinger-Robertson uncertainty relation of partially transposed su(1, 1) algebra operators, to detect the three-mode entanglement of non-Gaussian states of electromagnetic field. These operators are quadratic in mode creation and annihilation operators. The inseparability condition obtained using su(2) algebra operators is shown to guarantee the violation of stronger separability condition provided by Schrodinger-Robertson uncertainty relation of partially transposed su(1, 1) algebra operators. The obtained inseparability condition is also shown to be a necessary condition for W type entangled states and it is used to derive the general form for a family of such inseparability conditions. An experimental scheme is proposed to test the violation of separability condition. The results derived for three-mode systems are generalized to multimode systems.
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