Multipartite entanglement in 2 x 2 x n quantum systems

Abstract

We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of states, and they give rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W classes of 3 qubits. In particular, all 2 x 2 x n-states can be deterministically prepared from one maximally entangled state, and some applications like entanglement swapping are discussed.

9 pages, 3 eps figures

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• Entanglement Equivalence of $N$-qubit Symmetric States
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Multipartite entanglement in heterogeneous systems
• Multi-particle entanglement manipulation under positive partial transpose preserving operations
• Verifying multi-partite mode entanglement of W states
• Entanglement classes of permutation-symmetric qudit states: symmetric operations suffice
• The invariant-comb approach and its relation to the balancedness of multipartite entangled states
• Entanglement of four qubit systems: a geometric atlas with polynomial compass I (the finite world)
• Geometric descriptions of entangled states by auxiliaries varieties
• Range criterion and classification of true entanglement in $2\times M\times N$ system
• Classification of multipartite entanglement containing infinitely many kinds of states
• Matrix Pencils and Entanglement Classification
• Classification of Tripartite Entanglement with one Qubit
• Quantum Entanglement involved in Grover's and Shor's algorithms: the four-qubit case
• Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• Singularity of type $D_4$ arising from four qubit systems
• Genuine tripartite entanglement monotone of $(2\otimes 2\otimes n)-$ dimensional systems
• Existence of locally maximally entangled quantum states via geometric invariant theory
• Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts
• Classification of Bipartite and Tripartite Qutrit Entanglement under SLOCC
• Monogamy and entanglement in tripartite quantum states
• Nilpotent polynomials approach to four-qubit entanglement
• Concurrence classes for general pure multipartite states
• Learning Algebraic Models of Quantum Entanglement
• Exploring quantum properties of bipartite mixed states under coherent and incoherent basis
• Generation of entanglement via squeezing on a tripartite-optomechanical system
• Classification of multipartite systems featuring only $|W⟩$ and $|GHZ⟩$ genuine entangled states
• Concurrence classes for an arbitrary multi-qubit state based on positive operator valued measure
• Classification and Quantification of Entanglement Through Wedge Product and Geometry
• Many-body entanglement: Permutations and equivalence classes
• Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States
• Existence of maximally correlated states
• Analytically Computable Symmetric Quantum Correlations
• Candidate entanglement invariants for two Dirac spinors
• A type of localized quadripartite entanglement
• Characterization of multipartite entanglement in terms of local transformations
• Low degree Lorentz invariant polynomials as potential entanglement invariants for multiple Dirac spinors
• Genuinely multipartite entangled states in higher dimensions: a generalization of balancedness
• A Complete Set of Local Invariants for a Family of Multipartite Mixed States