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arXiv · 1012.2630

An algebraic classification of entangled states

Roman V. Buniy·Thomas W. Kephart
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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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Roman V. Buniy, Thomas W. Kephart. 2010-12-13. An algebraic classification of entangled states. https://doi.org/10.1088/1751-8113/45/18/185304

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