  We consider generalized Husimi distributions for many-body systems, and show
that their moments are good measures of complexity of many-body quantum states.
Our construction of the Husimi distribution is based on the coherent state of
the single-particle transformation group. Then the coherent states are
independent-particle states, and, at the same time, the most localized states
in the Husimi representation. Therefore delocalization of the Husimi
distribution, which can be measured by the moments, is a sign of many-body
correlation (entanglement). Since the delocalization of the Husimi distribution
is also related to chaoticity of the dynamics, it suggests a relation between
entanglement and chaos. Our definition of the Husimi distribution can be
applied not only to the systems of distinguishable particles, but also to those
of identical particles, i.e., fermions and bosons. We derive an algebraic
formula to evaluate the moments of the Husimi distribution.
