The problem of entanglement-assisted summation over a quantum multiple access channel ($\Sigma$ -QMAC) is intro-duced, involving $S$ servers, $K$ classical $(\mathbb{F}_{d})$ data streams that are replicated arbitrarily across various subsets of servers, and a receiver who wishes to compute the sum of the $K$ data streams. Independent of the data, entangled quantum systems $\mathcal{Q}_{1}, \mathcal{Q}_{2}, \cdots, \mathcal{Q}_{S}$ are prepared in advance and distributed to the corresponding servers. Each server $s, s\in[S]$ locally manipulates its quantum system $\mathcal{Q}_{s}$ according to its classical data and sends $\mathcal{Q}_{s}$ to the receiver. The total communication cost is $\log_{d}\vert \mathcal{Q}_{1}\vert +\log_{d}\vert \mathcal{Q}_{2}\vert +\cdots+\log_{d}\vert \mathcal{Q}_{S}\vert$ qudits, where $\vert \mathcal{Q}_{s}$ denotes the dimension of $\mathcal{Q}_{s}$. Based on a measurement of the composite system $\mathcal{Q}_{1}\mathcal{Q}_{2}\cdots \mathcal{Q}_{S}$, the receiver must recover the desired sum. The rate thus achieved is defined as the number of dits $(\mathbf{F}_{d}$ symbols) of the desired sum computed by the receiver per qudit (d-dimsional quantum system) of download. The capacity $C$ is the supremum of the set of all achievable rates. As the main result of this work, the precise capacity of $\Sigma$ -QMAC is obtained, from which it follows that quantum entanglements allow a factor of 2 gain in capacity (superdense coding gain) relative to capacity with no entanglements, in all cases (any $S, K, \mathbf{F}_{d}$ and any data replication pattern) provided that the entanglement-assisted capacity does not exceed 1 dit/qudit (Holevo bound). Coding schemes based on a recent $N$ -sum box abstraction are sufficient to achieve capacity.