Unique information lower-bound conjecture for the two-way secret key rate

Let $(S,Y,Z)$ be jointly distributed random variables. Write $UI(S;Y\backslash Z)$ for unique information of $Y$ about $S$ relative to $Z$, and let $S_{\leftrightarrow}\!\left({S};{Y}\!\left|{Z} \right. \right)$ denote the two-way secret key rate.

Unique information lower-bound conjecture. The unique information lower bounds the two-way secret key rate:

$$UI(S;Y\backslash Z) \le S_{\leftrightarrow}\!\left({S};{Y}\!\left|{Z} \right. \right).$$

The conjecture would identify unique information as a lower bound complementary to the known upper bounds on the two-way secret key rate. The paper notes that unique information is not generally an upper bound on the two-way rate, while the proposed lower-bound direction remains open.