Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix

Abstract

We study multipartite entanglement under stochastic local operations and classical communication (SLOCC) and propose the entanglement classification under SLOCC for arbitrary-dimensional multipartite ($n$-qudit) pure states via the rank of coefficient matrix, together with the permutation of qudits. The ranks of the coefficient matrices have been proved to be entanglement monotones. The entanglement classification of the $2\otimes 2\otimes 2\otimes 4$ system is discussed in terms of the generalized method, and 22 different SLOCC families are found.

6 pages, 3 figures, to be appeared in Journal of Physics A: Mathematical and Theoretical

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Cited by in corpus (7)

• Entanglement classification of 2 X 2 X 2 X d quantum systems via the ranks of the multiple coefficient matrices
• Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices
• Stochastic local operations and classical communication (SLOCC) and local unitary operations (LU) classifications of n qubits via ranks and singular values of the spin-flipping matrices
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• A generalization of Schmidt number for multipartite states
• Multipartite entanglement classes of a multiport beam-splitter
• Classification of the Entangled States of $2\times L\times M\times N\times H$