Quantum Private Membership Aggregation
Alptug Aytekin, Mohamed Nomeir, Sennur Ulukus
TL;DR
The paper addresses private aggregation of element frequencies across $N$ parties using quantum entanglement to privately compute the incidence-frequency vector over a universal set $\mathcal{K}$. It introduces a phase-encoded scheme based on an entangled $N$-qudit state and Sylvester clock operations, with a leader performing decoding via a tailored partial PVM to recover the aggregate while preserving individual privacy. A key result bounds the download cost by $D^* \le (N-1)K \log P^*$, where $P^*$ is the smallest prime not less than $N$, and a representative example illustrates the encoding/decoding workflow. The scheme also yields private summation modulo $P$, and the conclusions discuss limitations to field-based Fourier states and prospects for extending to ring/group structures in future work.
Abstract
We consider the problem of private set membership aggregation of $N$ parties by using an entangled quantum state. In this setting, the $N$ parties, which share an entangled state, aim to \emph{privately} know the number of times each element (message) is repeated among the $N$ parties, with respect to a universal set $\mathcal{K}$. This problem has applications in private comparison, ranking, voting, etc. We propose an encoding algorithm that maps the classical information into distinguishable quantum states, along with a decoding algorithm that exploits the distinguishability of the mapped states. The proposed scheme can also be used to calculate the $N$ party private summation modulo $P$.