Multipartite quantum correlation and entanglement in four-qubit pure states

Abstract

Based on the quantitative complementarity relations, we analyze thoroughly the properties of multipartite quantum correlations and entanglement in four-qubit pure states. We find that, unlike the three-qubit case, the single residual correlation, the genuine three- and four-qubit correlations are not suited to quantify entanglement. More interestingly, from our qualitative and numerical analysis, it is conjectured that the sum of all the residual correlations may constitute a good measure for the total multipartite entanglement in the system.

7 pages, 3 figues

References in corpus (24)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Introducing Quantum Discord
• Three qubits can be entangled in two inequivalent ways
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• Classical, quantum and total correlations
• Quantifying Entanglement
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Four qubits can be entangled in nine different ways
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Fidelity and Concurrence of conjugated states
• A potential multipartide entanglement measure
• Normal forms and entanglement measures for multipartite quantum states
• Entangled three-qubit states without concurrence and three-tangle
• Generic entanglement generation, quantum statistics and complementarity
• Quantification of complementarity in multi-qubit systems
• A new type of complementarity between quantum and classical information
• Geometric phase of an atom in a magnetic storage ring
• Multipartite pure-state entanglement and the generalized GHZ states
• Complementarity relations for multi-qubit systems
• Information-Theoretic Measure of Genuine Multi-Qubit Entanglement
• Fidelity, entanglement, and information complementarity relation

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• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Multipartite entanglement in four-qubit cluster-class states
• Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
• An Experimentally accessible geometric measure for entanglement in $N$-qubit pure states
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Decoherence-free preparation of Dicke states of trapped ions by collective stimulated Raman adiabatic passage
• Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits
• Efficient numerical method to calculate three-tangle of mixed states
• Entanglement in a class of multiqubit mixed states without multipartite tangles
• Permutation-invariant monotones for multipartite entanglement characterization
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• Entanglement evolution in multipartite cavity-reservoir systems under local unitary operations
• Entanglement evolution of three-qubit mixed states in multipartite cavity-reservoir systems
• Monogamy Inequality and Residual Entanglement of Three Qubits under Decoherence
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• Multi-linear Monogamy Relations for Three Qubit States
• Quantum entanglement in finite-dimensional Hilbert spaces
• Entanglement and measurement-induced nonlocality of mixed maximally entangled states in multipartite dynamics
• Correlation evolution and monogamy of two geometric quantum discords in multipartite systems
• Tighter monogamy relations in multiparty quantum systems
• Testing the Monogamy Relations via Rank-2 Mixtures
• A study of two-qubit density matrices with fermionic purifications