The authors prove a decomposition theorem for algebraic entanglement invariants of tripartite qudit states and use it to enumerate all entanglement classes for three qutrits.
An algebraic classification of entangled states
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abstract
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.
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Tripartite entanglement of qudits
The authors prove a decomposition theorem for algebraic entanglement invariants of tripartite qudit states and use it to enumerate all entanglement classes for three qutrits.