Holographic inequalities and entanglement of purification
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Publication:1750857
DOI10.1007/JHEP03(2018)006zbMATH Open1388.81626arXiv1710.07643WikidataQ130156891 ScholiaQ130156891MaRDI QIDQ1750857
Author name not available (Why is that?)
Publication date: 23 May 2018
Published in: (Search for Journal in Brave)
Abstract: We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.
Full work available at URL: https://arxiv.org/abs/1710.07643
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