  We investigate the geometrical and combinatorial structures of multipartite
quantum systems based on conifold and toric variety. In particular, we study
the relations between resolution of conifold, toric variety, a separable state,
and a quantum entangled state for bipartite and multi-qubit states. For example
we show that the resolved or deformed conifold is equivalent with the space of
a pure entangled two-qubit state. We also generalize this result into
multi-qubit states.
