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In this paper, I will discuss the geometrical structures of multipartitequantum systems based on complex projective schemes. In particular, I willexplicitly construct multi-qubit states in terms of these schemes and alsodiscuss separability and entanglement of bipartite and multipartite quantumstates. These results give some geometrical insight to the fascinating quantummechanical phenomena of entanglement which is fundamentally important and hasmany applications in the field of quantum computing.

Complex projective scheme approach to the geometrical structures of multipartite quantum systems