Holographic proof of the strong subadditivity of entanglement entropy

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) (A) +S (A). Recently, a method has been found for computing entanglement entropies in any field theory for which there is a holographically dual gravity theory. We give a simple geometrical proof of strong subadditivity employing this holographic prescription.