Entanglement of purification through holographic duality

Entanglement of purification through holographic duality The gauge/gravity correspondence discovered two decades ago has had a profound influence on how the basic laws in physics should be formulated. In spite of the predictive power of holographic approaches (for example, when they are applied to strongly coupled condensed-matter physics problems), the fundamental reasons behind their success remain unclear. Recently, the role of quantum entanglement has come to the fore. Here we explore a quantity that connects gravity and quantum information in the light of the gauge/gravity correspondence. This is given by the minimal cross-section of the entanglement wedge that connects two disjoint subsystems in a gravity dual. In particular, we focus on various inequalities that are satisfied by this quantity. They suggest that it is a holographic counterpart of the quantity called entanglement of purification, which measures a bipartite correlation in a given mixed state. We give a heuristic argument that supports this identification based on a tensor network interpretation of holography. This predicts that the entanglement of purification satisfies the strong superadditivity for holographic conformal field theories. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nature Physics Springer Journals

Entanglement of purification through holographic duality

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Publisher
Nature Publishing Group UK
Copyright
Copyright © 2018 by The Author(s)
Subject
Physics; Physics, general; Theoretical, Mathematical and Computational Physics; Classical and Continuum Physics; Atomic, Molecular, Optical and Plasma Physics; Condensed Matter Physics; Complex Systems
ISSN
1745-2473
eISSN
1745-2481
D.O.I.
10.1038/s41567-018-0075-2
Publisher site
See Article on Publisher Site

Abstract

The gauge/gravity correspondence discovered two decades ago has had a profound influence on how the basic laws in physics should be formulated. In spite of the predictive power of holographic approaches (for example, when they are applied to strongly coupled condensed-matter physics problems), the fundamental reasons behind their success remain unclear. Recently, the role of quantum entanglement has come to the fore. Here we explore a quantity that connects gravity and quantum information in the light of the gauge/gravity correspondence. This is given by the minimal cross-section of the entanglement wedge that connects two disjoint subsystems in a gravity dual. In particular, we focus on various inequalities that are satisfied by this quantity. They suggest that it is a holographic counterpart of the quantity called entanglement of purification, which measures a bipartite correlation in a given mixed state. We give a heuristic argument that supports this identification based on a tensor network interpretation of holography. This predicts that the entanglement of purification satisfies the strong superadditivity for holographic conformal field theories.

Journal

Nature PhysicsSpringer Journals

Published: Mar 26, 2018

References

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