Holographic proof of the strong subadditivity of entanglement entropy

Matthew Headrick, Tadashi Takayanagi
2007 Physical Review D  
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) > S(A ∪ B) + S(A ∩ 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
more » ... ong subadditivity employing this holographic prescription.
doi:10.1103/physrevd.76.106013 fatcat:nglhcxs64ffedpbk4grx2zn3dq