Quantum private set intersection with correlated sum using single photons

Secure multi-party computation (SMC) enables multiple parties to collaboratively perform computational tasks without revealing their private data. A speci¯c application scenario within SMC is Private Set Intersection with Correlated Sum (PSI-CS), where two participating parties compute the sum of associated elements in their intersection while preserving the privacy of their individual sets. This problem arises in various contexts, including calculating conversion amounts between suppliers and platforms, such as advertising conversion amounts and agency business conversion amounts. The paper proposes a protocol that employs quantum single-photon technology to compute the PSI-CS, provides four technical solutions suitable for various scenarios ranging from small to large data volumes, sparse to dense datasets, and without revealing the cardinality of the intersection. Additionally, the method extends to computing the union set with correlated sums. We experimentally validate the proposed protocol, conduct correctness and security analyses, and demonstrate its practical signi¯cance and application value. By utilizing single-photon technology, quantum gate operations, and measurements become more accessible, simplifying the protocol's implementation. Notably, our approach provides unconditional security against quantum computational attacks, representing a substantial improvement in both e±ciency and practical applicability compared to classical domain protocols.