A geometric approach to investigation of quantum entanglement is advocated.
We discuss first the geometry of the (N^2-1)--dimensional convex body
of  mixed quantum states acting  on an N--dimensional Hilbert space
and study projections of this set into 2- and 3-dimensional spaces.
For composed dimensions, N=K^2, one consideres the subset
of separable states and shows that it has a positive measure.
Analyzing its properties contributes to our understanding of
quantum entanglement and its time evolution.


Talk Number PIRSA:16120010
Speaker Profile Karol Zyczkowski
Collection Quantum Foundations