Bell-Type Inequalities to Detect True<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">n</mml:mi></mml:math>-Body Nonseparability

We analyze the structure of correlations among more than two quantum systems. We introduce a classification of correlations based on the concept of nonseparability, which is different a priori from the concept of entanglement. Generalizing a result of Svetlichny [Phys. Rev. D 35, 3066 (1987)] on three-particle correlations, we find an inequality for n-particle correlations that holds under the most general separability condition and that is violated by some quantum-mechanical states.