Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 3, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP03(2018)006
Keywords
AdS-CFT Correspondence; Gauge-gravity correspondence
Categories
Funding
- Berkeley Center for Theoretical Physics
- National Science Foundation [PHY-1521446, 82248-13067-44-PHPXH]
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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.
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