12 problems

Let $\upsilon,\upsilon_2,\upsilon_3,\ldots$ be the weighted-average ITV family defined in the source, and let the row-column-type transformations be the transformations on the tran…

Let $XYZ$ be the distribution displayed in the source, depending on a parameter $a$. The candidate-distribution binarization conjecture. There exists a value $a$ such that, for eve…

Let $a_{ij}:=P_{\overline{Y^2}|Y^2}(0,rs)$ for $r,s\in\{1,2,3\}$, and define $\tau_2$ on the indicated set by … where $j=\left\lceil i/2\right\rceil$ for $1\leq i\leq6$, and … The…

Let $X,Y,Z$ have the distribution specified in the source, with $Z$ determined by $X$ and $Y$ according to the displayed table. For $N\geq1$, let $\overline{Y^N}$ be any binary out…

Let $X,Y,Z$ be jointly distributed, and let $\overline{X}$ and $\overline{Y}$ be binary outputs of arbitrary binary output channels applied to $X$ and $Y$. For $N\geq 1$, let…

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 conjectur…

Let $P_{XYZ}$ be a probability distribution. The Renner–Wolf conjecture. … The reduced intrinsic information is a known upper bound on the secret-key rate and can be strictly small…

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

Let $R_{\op{S}}$ be the minimum communication rate required to achieve the secrecy capacity in the secret-key agreement model. A trusted helper is a user whose source is trusted an…

Let $X_{\mathcal{M}}$ be a hypergraphical source, and let $R_{\mathrm{SK}}$ denote the minimum communication rate required to achieve secret-key capacity. Theorem gives an upper bo…

Supporting-functional inequality.

Omnivocality conjecture. Omnivocal communication is necessary for achieving SK capacity if and only if the singleton partition is the unique minimizer for $\mathbf{I}(X_{[m]})$.