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：本文研究在量子擦除多址接入信道（QEMAC）上计算分布式信源经典求和所需的量子通信成本。$K$个经典消息分布在$S$个服务器之间，这些服务器预先共享量子纠缠。每个服务器$s\in[S]$对其量子子系统$\mathcal{Q}_s$进行操作并发送给接收方，接收方计算消息的总和。来自服务器$s\in[S]$的下载成本是$\mathcal{Q}_s$维度的对数。速率$R$定义为接收方计算出的求和实例数除以所有服务器的总下载成本。在对称设置下，令$K={S \choose \alpha}$个消息，每个消息被复制到一个由$\alpha$个服务器构成的唯一子集中，并且来自任意$\beta$个服务器的答案可能被擦除，我们证明容量（最大速率）为$C= \max\left\{ \min \left\{ \frac{2(\alpha-\beta)}{S}, \frac{S-2\beta}{S} \right\}, \frac{\alpha-\beta}{S} \right\}$。