The bound-secrecy conjecture

Let $X,Y,Z$ be jointly distributed random variables, and let $S(X:Y||Z)$ denote the secret-key rate and $I(X:Y \downarrow Z)$ the intrinsic information. The bound-secrecy conjecture. There exists a distribution $P_{XYZ}$ such that

$$I(X:Y \downarrow Z)>0 \quad\text{but}\quad S(X:Y||Z)=0.$$

Such a distribution would exhibit secrecy between Alice and Bob that cannot be extracted as a secret key. The paper discusses bound secrecy as a significant open problem and notes that evidence for its existence would imply that the reduced-intrinsic-information equality conjecture is false.