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Holographic Inequalities and Entanglement of Purification
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Holographic Inequalities and Entanglement of Purification
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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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Cited by 1 Pith paper
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Diagnosing Critical Behavior in AdS Einstein-Maxwell-Scalar Theory via Holographic Entanglement Measures
In the EMS holographic model, entanglement entropy, mutual information, wedge cross-section, and butterfly velocity all show critical exponent 1—twice the scalar order parameter—and MI grows faster than EWCS across th...
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