4 problems

Let $X_1,X_2$ be binary random variables with quantum side information $B_1,B_2$, and let $\tau$ denote the product construction in which the output is $X_1+X_2$. Write…

Let $X_1,X_2$ be binary random variables with quantum side information $B_1,B_2$, let $\rho_1,\rho_2$ denote their respective classical–quantum states, and let $X_1+X_2$ be their s…

Let $h_\alpha$ denote the binary conditional Rényi-entropy function and let $\ast$ denote binary convolution. There exists a value $1<\hat\alpha<1.3863$ such that … is convex for…

Let $k_\alpha^A$ denote the Arimoto conditional-entropy function and let $\ast$ denote binary convolution. There exists a value $1<\hat\alpha<1.5783$ such that … is convex for…