We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions. We also obtain an entanglement classification of four qubits, where we find 27 fundamental sets of classes.
Buniy, R.V., & Kephart, T.W. (2012). An algebraic classification of entangled states. Journal of Physics A, 45(18). doi: 10.1088/1751-8113/45/18/185304
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