Correlations Existing in Three-Qubit Product States

Analytic results of the relationship between local noncommutativity and non-violations of Svetlichny inequalities for three-qubit separable states are obtained. It is shown that the converse trade-off relations presented by Seevinck and Uffinck Phys. Rev. A 2007 76 042105 do not always hold for three-qubit states, and that there exists some correlation even though the state is the simple product state.