Entanglement of purification for multipartite states and its holographic dual
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Publication:1627379
DOI10.1007/JHEP10(2018)152zbMATH Open1402.81233arXiv1805.02625WikidataQ129031854 ScholiaQ129031854MaRDI QIDQ1627379
Author name not available (Why is that?)
Publication date: 22 November 2018
Published in: (Search for Journal in Brave)
Abstract: We introduce a new information-theoretic measure of multipartite quantum/classical correlations , by generalizing the entanglement of purification to multipartite states. We provide proofs of its various properties, focusing on several entropic inequalities, in generic quantum systems. In particular, it turns out that the multipartite entanglement of purification gives an upper bound on multipartite mutual information, which is a generalization of quantum mutual information in the spirit of relative entropy. After that, motivated by a tensor network description of the AdS/CFT correspondence, we also define a holographic dual of multipartite entanglement of purification , as a sum of minimal areas of codimension-2 surfaces which divide the entanglement wedge into multi-pieces. We prove that this geometrical quantity satisfies all properties we proved for the multipartite entanglement of purification. These agreements strongly support the conjecture. We also show that the multipartite entanglement of purification gives an upper bound on multipartite squashed entanglement, which is a promising measure of multipartite quantum entanglement. We discuss potential saturation of multipartite squashed entanglement onto multipartite mutual information in holographic CFTs and its applications.
Full work available at URL: https://arxiv.org/abs/1805.02625
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