GENERALIZED COHERENT STATES ARE UNIQUE BELL STATES OF QUANTUM-SYSTEMSWITH LIE-GROUP SYMMETRIES

We consider quantum systems, whose dynamical symmetry groups are semis imple Lie groups, which can be split or decay into two subsystems of t he same symmetry. We prove that the only states of such a system that factorize upon splitting are the generalized coherent states. Since Be ll's inequality is never violated by the direct product state. when th e system prepared in the generalized coherent state is split, no quant um correlations are created. Therefore the generalized coherent states are the unique Bell states, i.e., the pure quantum states preserving the fundamental classical property of satisfying Bell's inequality upo n splitting.