Determining lower bounds on a measure of multipartite entanglement from few local observables

Abstract

We introduce a method to lower bound an entropy-based measure of genuine multipartite entanglement via nonlinear entanglement witnesses. We show that some of these bounds are tight and explicitly work out their connection to a framework of nonlinear witnesses that were published recently. Furthermore we provide a detailed analysis of these lower bounds in the context of other possible bounds and measures. In exemplary cases we show that only a few local measurements are necessary to determine these lower bounds.

arXiv comment11 pages, 2 figures

References in corpus (22)

• Quantum entanglement
• Entanglement detection
• Optimization of entanglement witnesses
• Classification of mixed three-qubit states
• A Schmidt number for density matrices
• Sustained Quantum Coherence and Entanglement in the Avian Compass
• Taming multiparticle entanglement
• Separability criteria for genuine multiparticle entanglement
• Measure of genuine multipartite entanglement with computable lower bounds
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• I-concurrence and tangle for isotropic states
• Entanglement Dynamics of Two Qubits in a Common Bath
• Nonlinear entanglement witnesses
• Multipartite entanglement in quantum algorithms
• Multipartite entanglement in quantum spin chains
• Characterizing and Quantifying Frustration in Quantum Many-Body Systems
• Experimentally Feasible Security Check for n-qubit Quantum Secret Sharing
• Multipartite entanglement measure for all discrete systems
• Solving the liar detection problem using the four-qubit singlet state
• Two computable sets of multipartite entanglement measures
• Multipartite Entanglement and Quantum State Exchange
• Examining the dimensionality of genuine multipartite entanglement

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