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Inductive classification of multipartite entanglement under SLOCC

L. Lamata·J. Leon·D. Salgado·E. Solano
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Abstract

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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L. Lamata, J. Leon, D. Salgado, E. Solano. 2006-10-27. Inductive classification of multipartite entanglement under SLOCC. https://doi.org/10.1103/physreva.74.052336

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