Inspired by a recent study by Christensen and Popovski on secure $2$-user product computation for finite-fields of prime-order over a quantum multiple access channel (QMAC), the generalization to $K$ users and arbitrary finite fields is explored. Combining ideas of batch-processing, quantum $2$-sum protocol, a secure computation scheme of Feige, Killian and Naor (FKN), a field-group isomorphism and additive secret sharing, asymptotically optimal (capacity-achieving for large alphabet) schemes are proposed for secure $K$-user (any $K$) product computation over any finite field. The capacity of modulo-$d$ ($d\geq 2$) secure $K$-sum computation over the QMAC is found to be $2/K$ computations/qudit as a byproduct of the analysis.

翻译：受Christensen与Popovski近期关于量子多址信道（QMAC）上素数阶有限域中安全$2$用户乘积计算研究的启发，本文探讨了该问题向$K$用户及任意有限域的推广。通过结合批处理、量子$2$-求和协议、Feige-Killian-Naor（FKN）安全计算方案、域-群同构及加法秘密共享等思想，提出了在任意有限域上实现安全$K$用户（任意$K$）乘积计算的渐近最优方案（在大字母表条件下达到容量）。作为分析副产品，确定了QMAC上模$d$（$d\geq 2$）安全$K$-求和计算的容量为$2/K$计算/量子比特。