  We present a description of entanglement in composite quantum systems in
terms of symplectic geometry. We provide a symplectic characterization of sets
of equally entangled states as orbits of group actions in the space of states.
In particular, using Kostant-Sternberg theorem, we show that separable states
form a unique Kaehler orbit, whereas orbits of entanglement states are
characterized by different degrees of degeneracy of the canonical symplectic
form on the complex projective space. The degree of degeneracy may be thus used
as a new geometric measure of entanglement and we show how to calculate it for
various multiparticle systems providing also simple criteria of separability.
The presented method is general and can be applied also under different
additional symmetry conditions stemming, eg. from the indistinguishability of
particles.
