Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 33 / 5 / a / 1

Expand the difference between the two quantum mutual informations:This is precisely the nonnegative expression in Strong subadditivity of Von Neumann entropy. ThusThe reduced state on $AB$ is obtained by the partial trace over $C$, so this proves that discarding a system cannot increase its quantum mutual information with the retained reference.