Renner–Wolf conjecture on reduced intrinsic information and secret-key rate

Let $P_{XYZ}$ be a probability distribution. The Renner–Wolf conjecture.

$$S(X:Y||Z)=I(X:Y \downarrow \downarrow Z).$$

The reduced intrinsic information is a known upper bound on the secret-key rate and can be strictly smaller than the intrinsic information. Equality would give a simple distribution-based characterization of the secret-key rate; the paper presents this as an open problem.