The quantum communication cost of computing a classical sum of distributed sources is studied over a quantum erasure multiple access channel (QEMAC). $K$ messages are distributed across $S$ servers so that each server knows a subset of the messages. Each server $s\in[S]$ sends a quantum subsystem $\mathcal{Q}_s$ to the receiver who computes the sum of the messages. The download cost from Server $s\in [S]$ is the logarithm of the dimension of $\mathcal{Q}_s$. The rate $R$ is defined as the number of instances of the sum computed at the receiver, divided by the total download cost from all the servers. In the symmetric setting with $K= {S \choose \alpha} $ messages where each message is replicated among a unique subset of $\alpha$ servers, and the answers from any $\beta$ servers may be erased, the rate achieved is $R= \max\left\{ \min \left\{ \frac{2(\alpha-\beta)}{S}, 1-\frac{2\beta}{S} \right\}, \frac{\alpha-\beta}{S} \right\}$, which is shown to be optimal when $S\geq 2\alpha$.

翻译：研究了在量子擦除多址接入信道（QEMAC）上计算分布式信源经典和的量子通信成本。$K$条消息分布在$S$个服务器上，每个服务器知道这些消息的一个子集。每个服务器$s\in[S]$将一个量子子系统$\mathcal{Q}_s$发送给接收方，接收方计算消息的和。从服务器$s\in [S]$下载的成本是$\mathcal{Q}_s$维度的对数。速率$R$定义为接收方计算出的和的实例数除以所有服务器的总下载成本。在对称场景中，$K= {S \choose \alpha} $条消息，每条消息在$\alpha$个服务器的唯一子集上复制，并且来自任意$\beta$个服务器的答案可能被擦除，所达到的速率为$R= \max\left\{ \min \left\{ \frac{2(\alpha-\beta)}{S}, 1-\frac{2\beta}{S} \right\}, \frac{\alpha-\beta}{S} \right\}$，当$S\geq 2\alpha$时，该速率被证明是最优的。