1012.2630 (Roman V. Buniy et al.)

An algebraic classification of entangled states    [PDF]

Roman V. Buniy, Thomas W. Kephart

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.

View original: http://arxiv.org/abs/1012.2630