Genuine multipartite entanglement detection and lower bound of multipartite concurrence

Abstract

The problems of genuine multipartite entanglement detection and classification are challenging. We show that a multipartite quantum state is genuine multipartite entangled if the multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine multipartite entanglement. Then, we present a lower bound of the multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and classify the genuine multipartite entanglement. As applications, the genuine multipartite entanglement of tripartite systems is analyzed in detail.

7 pages

References in corpus (21)

• Entanglement in continuous variable systems: Recent advances and current perspectives
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Taming multiparticle entanglement
• Concurrence of arbitrary dimensional bipartite quantum states
• Measure of genuine multipartite entanglement with computable lower bounds
• Lower bounds on concurrence and separability conditions
• Witnessing genuine multipartite entanglement with positive maps
• Optimal entanglement witnesses based on local orthogonal observables
• Measuring Multipartite Concurrence with a Single Factorizable Observable
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Determining lower bounds on a measure of multipartite entanglement from few local observables
• Further results on entanglement detection and quantification from the correlation matrix criterion
• Characterizing multipartite entanglement without shared reference frames
• A lower bound of concurrence for multipartite quantum states
• Improved lower bounds on genuine-multipartite-entanglement concurrence
• Lower Bounds of Concurrence for Tripartite Quantum Systems
• An Experimentally accessible geometric measure for entanglement in $N$-qubit pure states
• Entanglement Enhances Security in Secret Sharing
• Detecting genuine multipartite entanglement of pure states with bipartite correlations
• Bell inequalities for multipartite qubit quantum systems and their maximal violation
• Lower Bound of Multipartite Concurrence Based on Sub-quantum State Decomposition

Cited by in corpus (17)

• General Monogamy of Tsallis $q$-Entropy Entanglement in Multiqubit Systems
• A Brief Overview of Bipartite and Multipartite Entanglement Measures
• Measure and detection of genuine multipartite entanglement for tripartite systems
• The norms of Bloch vectors and classification of four qudits quantum states
• A lower bound of concurrence for multipartite quantum systems
• Analytical Expression of Quantum Discord for Rank-2 Two-qubit States
• Quantum Fisher information-based detection of genuine tripartite entanglement
• Detection of Genuine Multipartite Entanglement in Multipartite Systems
• Detection of mixed bipartite entangled state in arbitrary dimension via structural physical approximation of partial transposition
• Bounds on Multipartite Concurrence and Tangle
• Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor
• Quantum Information Aspects on Bulk and Nano Interacting Fermi System: Spin-Space Density Matrix Approach
• Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity
• On genuine entanglement for tripartite systems
• Projection based lower bounds of concurrence for multipartite quantum systems
• Uniform Entanglement Frames
• Characterizing multipartite entanglement by violation of CHSH inequalities