On the Capacity of Secure K-user Product Computation over a Quantum MAC

05/31/2023

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by   Yuxiang Lu, et al.

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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.