Measure of multipartite entanglement with computable lower bounds

Abstract

In this paper, we present a measure of multipartite entanglement ($k$-nonseparable), $k$-ME concurrence $C_{k-\mathrm{ME}}(\rho )$ that unambiguously detects all $k$-nonseparable states in arbitrary dimensions, where the special case, 2-ME concurrence $C_{2-\mathrm{ME}}(\rho )$, is a measure of genuine multipartite entanglement. The new measure $k$-ME concurrence satisfies important characteristics of an entanglement measure including entanglement monotone, vanishing on $k$-separable states, convexity, subadditivity and strictly greater than zero for all $k$-nonseparable states. Two powerful lower bounds on this measure are given. These lower bounds are experimentally implementable without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed. We illustrate detailed examples in which the given bounds perform better than other known detection criteria.

12 pages, 3 figures

References in corpus (14)

• Entanglement detection
• Entanglement versus Correlations in Spin Systems
• Quantum information with Gaussian states
• Measure of genuine multipartite entanglement with computable lower bounds
• Deterministic secure direct communication using GHZ states and swapping quantum entanglement
• Optimal Controlled Teleportation
• Multipartite entanglement detection via structure factors
• Improved lower bounds on genuine-multipartite-entanglement concurrence
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations
• Two Local Observables are Sufficient to Characterize Maximally Entangled States of N Qubits
• Separability criteria for several classes of $n$-partite quantum states
• Two computable sets of multipartite entanglement measures
• Experimentally implementable criteria revealing substructures of genuine multipartite entanglement

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