Three-sender quantum simultaneous decoding conjecture for multiple access channels

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 $\rho^B_{x_1,x_2,x_3}$. For $i\in\{1,2,3\}$, let $\{X_i^n(m_i)\}_{m_i\in\mathcal{M}_i}$ be random codebooks generated according to the product distributions $p^n_{X_i^n}$, with message sets $\mathcal{M}_i=\{1,\ldots,2^{n(R_i-\delta)}\}$ and $\delta>0$. Three-sender QMAC simultaneous decoding conjecture. There exists a simultaneous decoding POVM $\{\Lambda_{m_1,m_2,m_3}\}$ whose expected average probability of error is at most $\epsilon$ for all $\epsilon,\delta>0$ and sufficiently large $n$, for every rate triple $(R_1,R_2,R_3)\in\mathcal{C}_{\textrm{3MAC}}$. This conjectures a simultaneous decoder for the three-sender quantum multiple access channel, extending the established two-sender coding result; whether such a decoder exists for every rate triple in the full capacity region is the remaining issue.