5 problems

Achievability conjecture. There exists a positive number $P^*(K)$ such that, for every $P\geq P^*(K)$, one can choose real numbers $\beta_2,\ldots,\beta_K$ with $|\beta_k|\geq 1$ s…

Necessity conjecture for preservation of $IS$. If $IS$ is preserved by the polarization process, then such a subspace $V_S$ must exist. The condition is presented as necessary for…

Let $\mathcal{C}_{\textrm{3MAC}}$ denote the capacity region of a ccc-q multiple access channel with three senders, whose inputs $x_1,x_2,x_3$ produce the quantum state…

Existence of a three-sender quantum simultaneous decoder. There exists a decoding POVM $\{\Lambda_{l,m,k}\}_{l,m,k}$ such that, for every $\epsilon>0$ and sufficiently large $n$, t…

Let the Gaussian doubly-dirty multiple access channel have high signal-to-noise ratio and strong interference. Denote its sum capacity by $C^{\sum}$ and the sum rate of the best kno…