Inductive classification of multipartite entanglement under SLOCC

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.

11 pages and no figures. Accepted in PRA

References in corpus (3)

• DMRG and periodic boundary conditions: a quantum information perspective
• Constructing N-qubit entanglement monotones from anti-linear operators
• Operational Classification and Quantification of Multipartite Entangled States

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• Permutation-invariant monotones for multipartite entanglement characterization
• Compatibility conditions from multipartite entanglement measures
• A Complete Set of Local Invariants for a Family of Multipartite Mixed States
• Fully multi-qubit entangled states