An algebraic classification of entangled states

Details An algebraic classification of entangled states An algebraic classification of entangled states

2010-12-13

arxiv.org/abs/1012.2630v1

Physics

Quantum Physics

20 pages, 11 tables, 2 figures

Scientific paper

We provide a classification of entangled states that is based on the analysis of algebraic properties of linear maps associated with the states. The kernels of the maps define algebraic invariants, which are new discrete measures of entanglement. 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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