Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix

Abstract

We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient matrices associated with the states. The rank of the coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes, as exemplified here. When applied to the symmetric states, this approach reveals that all the Dicke states |l,n> with l=1, ..., [n/2] are inequivalent under SLOCC.

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Cited by in corpus (29)

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• Quantifying entanglement resources
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• Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
• Deterministic generation of arbitrary symmetric states and entanglement classes
• Entanglement Classification of Four-partite States under the SLOCC
• Entanglement classification of 2 X 2 X 2 X d quantum systems via the ranks of the multiple coefficient matrices
• Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• Quantum State Concentration and Classification of Multipartite Entanglement
• Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices
• An Algebraic-Geometric Characterization of Tripartite Entanglement
• 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
• Detecting genuine multipartite correlations in terms of the rank of coefficient matrix
• Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• Local unitary invariants for multipartite states
• Classification and Quantification of Entanglement Through Wedge Product and Geometry
• Classification witness operator for the classification of different subclasses of three-qubit GHZ class
• Geometric genuine multipartite entanglement for four-qubit systems
• Sequential generation of Polynomial Invariants and N-body non-local correlations
• A generalization of Schmidt number for multipartite states
• Multipartite States under Elementary Local Operations
• Classifying Entanglement by Algebraic Geometry
• Multipartite entanglement classes of a multiport beam-splitter
• Critical behaviour in the optimal generation of multipartite entanglement
• Entanglement classification via integer partitions
• Classification of the Entangled States of $2\times L\times M\times N\times H$