  The unique information ($UI$) is an information measure that quantifies a
deviation from the Blackwell order. We have recently shown that this quantity
is an upper bound on the one-way secret key rate. In this paper, we prove a
triangle inequality for the $UI$, which implies that the $UI$ is never greater
than one of the best known upper bounds on the two-way secret key rate. We
conjecture that the $UI$ lower bounds the two-way rate and discuss implications
of the conjecture.
