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arXiv:1701.04155 · Journal of Physics A Mathematical and Theoretical

Entanglement classification of four-partite states under the SLOCC

S. M. Zangi, Junli Li, Cong‐Feng Qiao

Published Jun 19, 2017• 19 citations
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Abstract

Abstract We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two tripartite states and a bipartite state, the entanglement classification is reduced to the classification of tripartite and bipartite entanglements. This reduction method has the merit of involving only the linear constrains, and meanwhile provides an insight into the entanglement character of the subsystems.

DOI
10.1088/1751-8121/aa7a2d

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We propose an inductive procedure to classify NNN-partite entanglement under stochastic local operations and classical communication provided such a classification is known for $N\ensuremath{-}1$ 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 bipartite 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 NNN-partite entanglement classes in terms of the number of entanglement classes for $N\ensuremath{-}1$ qubits.