Quantifying Tri-partite Entanglement with Entropic Correlations

Abstract

We show how to quantify tri-partite entanglement using entropies derived from experimental correlations. We use a multi-partite generalization of the entanglement of formation that is greater than zero if and only if the state is genuinely multi-partite entangled. We develop an entropic witness for tripartite entanglement, and show that the degree of violation of this witness places a lower limit on the tripartite entanglement of formation. We test our results in the three-qubit regime using the GHZ-Werner state and the W-Werner state, and in the high-dimensional pure-state regime using the triple-Gaussian wavefunction describing the spatial and energy-time entanglement in photon triplets generated in third-order spontaneous parametric down-conversion. In addition, we discuss the challenges in quantifying the entanglement for progressively larger numbers of parties, and give both entropic and target-state-based witnesses of multi-partite entanglement that circumvent this issue.

arXiv comment14 pages, 6 figures (removed inequality (formerly appendix B4) due to typo)

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• Multipartite Entanglement: A Journey Through Geometry
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• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Generation of entanglement via squeezing on a tripartite-optomechanical system
• A geometric formulation to measure global and genuine entanglement in three-qubit systems
• Quantifying Tripartite Spatial and Energy-Time Entanglement in Nonlinear Optics
• Detection of entanglement via moments of positive maps
• The Smallest Interacting Universe
• Sudden change of genuine multipartite entanglement in non-Markovian dynamics
• Error-mitigated inference of quantum network topology