4 problems

Let the noise modes c_i_{i=1}^n be in a product state … of $n$ vacuum states, and assume that $H(A^n)_\rho=n g(N_A)$. Minimum output-entropy conjecture. Then … This conjecture is…

Constrained minimum output entropy conjecture. The output entropy satisfies

Multimode constrained minimum output entropy conjecture. For every $m$-mode state $\rho$,

Let $S(\beta^{(t)})$ be a set such that, for every $\varepsilon>0$, the set $S(\beta^{(t)})+\varepsilon$ almost surely contains the eigenvalues of outputs of random quantum channel…