Classification of Tripartite Entanglement with one Qubit

Abstract

We present a method to find the decompositions of tripartite entangled pure states which are smaller than two successive Schmidt decompositions. The method becomes very simple when one of the subsystems is a qubit. In this particular case, we get a classification of states according to their decompositions. Furthermore, we also use this method to classify the entangled states that can be inter-converted through stochastic local operations and classical communication (SLOCC). More general tripartite systems are briefly discussed.

Revised version with a new title, a simplification in section III and added references

References in corpus (10)

• Decoherence, einselection, and the quantum origins of the classical
• Three qubits can be entangled in two inequivalent ways
• Four qubits can be entangled in nine different ways
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Characterizing Entanglement
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Classification of multipartite entangled states by multidimensional determinants
• Quantum inseparability as local pseudomixture
• Multipartite entanglement in 2 x 2 x n quantum systems
• Universal Measure of Entanglement

Cited by in corpus (14)

• Inductive Entanglement Classification of Four Qubits under SLOCC
• Multipartite monogamy of the concurrence
• Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
• Matrix Pencils and Entanglement Classification
• Entanglement classification of 2 X 2 X 2 X d quantum systems via the ranks of the multiple coefficient matrices
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• The Parametric Symmetry and Numbers of the Entangled Class of 2 \times M \times N System
• Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices
• A link between Quantum Entanglement, Secant varieties and Sphericity
• Classification of the Entangled States of $2\times N\times N$
• Entanglement criterion via general symmetric informationally complete measurement
• Classification of Bipartite and Tripartite Qutrit Entanglement under SLOCC
• Many-body entanglement: Permutations and equivalence classes
• A generalization of Schmidt number for multipartite states