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On the classification of pure multipartite states

The classification of quantum states into equivalence classes is considered. Two states are equivalent if local operations and classical communication suffice to transform one state to the other with a positive probability of success. Transformations of this kind are called SLOCC (stochastic local operations and classical communication). To achieve the goal of classification one has to identify invariants of the group of SLOCC operations that distinguish between non-equivalent states. This paper concerns n-qbit pure states with n>=3. A set of discrete invariants is derived, leading to an easily computable necessary condition for equivalence. The method can be generalized to handle entanglement of any finite level systems.