The quantum communication cost of computing a classical sum of distributed sources is studied over a quantum erasure multiple access channel (QEMAC). $K$ classical messages are distributed across $S$ servers, who also share quantum entanglement in advance. Each server $s\in[S]$ manipulates and sends its 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, we show that the capacity (maximal rate) is $C= \max\left\{ \min \left\{ \frac{2(\alpha-\beta)}{S}, \frac{S-2\beta}{S} \right\}, \frac{\alpha-\beta}{S} \right\}$.

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问题的量子通信代价。考虑$K$个经典消息分布在$S$个服务器上，各服务器预先共享量子纠缠。每个服务器$s\in[S]$操作其量子子系统$\mathcal{Q}_s$并发送给接收端，由接收端计算消息之和。服务器$s\in[S]$的下载代价定义为$\mathcal{Q}_s$维度的对数。速率$R$定义为接收端计算出的和实例数量除以所有服务器的总下载代价。在对称场景下，考虑$K= {S \choose \alpha}$个消息，每个消息被复制到唯一的一组$\alpha$个服务器中，且任意$\beta$个服务器的应答可能被擦除，我们证明容量（最大速率）为$C= \max\left\{ \min \left\{ \frac{2(\alpha-\beta)}{S}, \frac{S-2\beta}{S} \right\}, \frac{\alpha-\beta}{S} \right\}$。