Inspired by recent work by Christensen and Popovski on secure $2$-user product computation for finite-fields of prime-order over a quantum multiple access channel, the generalization to $K$ users and arbitrary finite fields is explored. Asymptotically optimal (capacity-achieving for large alphabet) schemes are proposed. Additionally, the capacity of modulo-$d$ ($d\geq 2$) secure $K$-sum computation is shown to be $2/K$ computations/qudit, generalizing a result of Nishimura and Kawachi beyond binary, and improving upon it for odd $K$.

翻译：受Christensen和Popovski近期关于量子多址信道上素数阶有限域安全$2$用户乘积计算工作的启发，本文探讨了该问题向$K$用户及任意有限域的推广。我们提出了渐近最优（在大字母表下可达容量）的方案。此外，对于模$d$（$d\geq 2$）安全$K$求和计算，我们证明了其容量为$2/K$计算/量子比特，这一结果将Nishimura和Kawachi的结论从二元情形推广至一般情形，并在$K$为奇数时优于原结论。