Communication Efficiency of Summation over a Quantum Erasure MAC with Replicated Inputs
Yuhang Yao, Syed A. Jafar · 2024
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$\mathrm{s}\in[S]$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$K=\left(_{\alpha}^{S}\right)$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$R=\max \left\{\min \left\{\frac{2(\alpha-\beta)}{S}, 1-\frac{2 \beta}{S}\right\}, \frac{\alpha-\beta}{S}\right\}$.