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.
Cite
@article{arxiv.2004.03579,
title = {Quantifying Tri-partite Entanglement with Entropic Correlations},
author = {James Schneeloch and Christopher C. Tison and Michael L. Fanto and Shannon Ray and Paul M. Alsing},
journal= {arXiv preprint arXiv:2004.03579},
year = {2020}
}
Comments
14 pages, 6 figures (removed inequality (formerly appendix B4) due to typo)