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≥2) secure K-sum computation over the QMAC is found to be
2/K computations/qudit as a byproduct of the analysis