Entanglement classification of 2 X 2 X 2 X d quantum systems via the ranks of the multiple coefficient matrices

Abstract

The coefficient matrix is an efficient tool in entanglement classification under stochastic local operation and classical communication. In this work, we take all the ranks of the coefficient matrices into account in the method of entanglement classification, and give the entanglement classification procedure for arbitrary-dimensional multipartite pure states under stochastic local operation and classical communication. As a main application, we study the entanglement classification for quantum systems in the Hilbert space $\mathcal{H}={\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^d$ in terms of the ranks of the coefficient matrices.

7 pages and 2 figures

References in corpus (10)

• Efficient Toffoli Gates Using Qudits
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• The structure of multidimensional entanglement in multipartite systems
• Four-qubit entanglement from string theory
• Inductive classification of multipartite entanglement under SLOCC
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• Tight Correlation-Function Bell Inequality for Multipartite $d$-Dimensional System
• Detecting genuine multipartite correlations in terms of the rank of coefficient matrix

Cited by in corpus (9)

• Multipartite entanglement in heterogeneous systems
• Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays
• Existence of locally maximally entangled quantum states via geometric invariant theory
• Quantum correlations in qutrit-qutrit systems under local quantum noise channels
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle
• Freudenthal ranks: GHZ vs. W