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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.
Forward citations
Cited by 2 Pith papers
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R\'enyi Entanglement of Purification and Half R\'enyi Reflected Entropy in Free Scalar Theory
In a free scalar lattice model, numerical calculations show Rényi entanglement of purification is at least half the Rényi reflected entropy for 0 < n < 2 in the small subsystems tested.
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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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