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arXiv · 0704.3719

A holographic proof of the strong subadditivity of entanglement entropy

Matthew Headrick·Tadashi Takayanagi
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Abstract

When a quantum system is divided into subsystems, their entanglement entropies are subject to an inequality known as "strong subadditivity". For a field theory this inequality can be stated as follows: given any two regions of space $A$ and $B$, $S(A) + S(B) \ge S(A \cup B) + S(A \cap B)$. Recently, a method has been found for computing entanglement entropies in any field theory for which there is a holographically dual gravity theory. In this note we give a simple geometrical proof of strong subadditivity employing this holographic prescription.

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Matthew Headrick, Tadashi Takayanagi. 2007-04-27. A holographic proof of the strong subadditivity of entanglement entropy. https://doi.org/10.1103/physrevd.76.106013

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