Entangled three-qubit states without concurrence and three-tangle

Abstract

We provide a complete analysis of mixed three-qubit states composed of a GHZ state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this ``monogamy'' can be lifted for mixed states by virtue of vanishing tangle measures.

10 RevTeX pages, 3 figures, abstract and conclusions substantially extended

References in corpus (20)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Three qubits can be entangled in two inequivalent ways
• Concentrating Partial Entanglement by Local Operations
• Distributed Entanglement
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Classification of mixed three-qubit states
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Fidelity and Concurrence of conjugated states
• Normal forms and entanglement measures for multipartite quantum states
• Separability and distillability of multiparticle quantum systems
• Classification of multipartite entangled states by multidimensional determinants
• Constructing N-qubit entanglement monotones from anti-linear operators
• Three-qubit pure-state canonical forms
• Local symmetry properties of pure 3-qubit states
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• Degree of entanglement for two qubits
• The twistor geometry of three-qubit entanglement
• A complete set of covariants of the four qubit system
• Existence Criterion of Genuine Tripartite Entanglement

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• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Entanglement monogamy and entanglement evolution in multipartite systems
• Exploring multipartite quantum correlations with the square of quantum discord
• Three-tangle for mixtures of generalized GHZ and generalized W states
• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
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• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
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• Multipartite quantum correlation and entanglement in four-qubit pure states
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• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
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• Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
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• Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
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• The rebit three-tangle and its relation to two-qubit entanglement
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• Strong monogamy inequalities for four qubits
• A study of separability criteria for mixed three-qubit states
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• Tripartite entanglement of fermionic system in accelerated frames
• Rescaling multipartite entanglement measures for mixed states
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• Invariant-based entanglement monotones as expectation values and their experimental detection
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• Tripartite Entanglement Dynamics in the presence of Non-Markovian Environment
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• Tripartite Entanglement-Dependence of Tripartite Non-locality in Non-inertial Frame
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• Monogamy Inequality and Residual Entanglement of Three Qubits under Decoherence
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• Exact zeros of entanglement for arbitrary rank-two mixtures: how a geometric view of the zero-polytope makes life more easy
• SL-invariant entanglement measures in higher dimensions: the case of spin $1$ and $3/2$
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