On the Capacity of Secure K-User Product Computation Over a Quantum MAC

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
$K$
.