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It has been observed that the reduced density matrices of bipartite quditpure states possess a Gram matrix structure. This observation has opened apossibility of analysing the entanglement in such systems from the purelygeometrical point of view. In particular, a new quantitative measure of anentanglement of the geometrical nature, has been proposed. Using the inventedGram matrix approach, a version of a non-linear purification of mixed statesdescribing the system analysed has been presented.

A Gramian Approach to Entanglement in Bipartite Finite Dimensional Systems: The case of pure states