Inductive classification of multipartite entanglement under SLOCC

Details Inductive classification of multipartite entanglement under SLOCC Inductive classification of multipartite entanglement under SLOCC

2006-03-27

arxiv.org/abs/quant-ph/0603243v2

Phys. Rev. A 74, 052336 (2006)

Physics

Quantum Physics

11 pages and no figures. Accepted in PRA

Scientific paper

10.1103/PhysRevA.74.052336

We propose an inductive procedure to classify N-partite entanglement under stochastic local operations and classical communication (SLOCC) provided such a classification is known for N-1 qubits. The method is based upon the analysis of the coefficient matrix of the state in an arbitrary product basis. We illustrate this approach in detail with the well-known bi- and tripartite systems, obtaining as a by-product a systematic criterion to establish the entanglement class of a given pure state without resourcing to any entanglement measure. The general case is proved by induction, allowing us to find an upper bound for the number of N-partite entanglement classes in terms of the number of entanglement classes for N-1 qubits.

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