Holographic inequalities and entanglement of purification

A bstract 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 tr...

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Bibliographic Details
Published in:The journal of high energy physics 2018-03, Vol.2018 (3), p.1-17, Article 6
Main Authors: Bao, Ning, Halpern, Illan F.
Format: Article
Language:English
Subjects:
AdS-CFT Correspondence
Classical and Quantum Gravitation
Cross-sections
Elementary Particles
Gauge-gravity correspondence
High energy physics
Inequalities
Information theory
Lower bounds
Physics
Physics and Astronomy
Purification
Quantum entanglement
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Upper bounds
Wedges
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP03(2018)006