Multi-user semi-device independent quantum private query

Existing quantum private query (QPQ) proposals are mostly for single-user scenarios, while recent multi-user proposals assume the existence of a semi-trusted server and only consider the retrieval of the items of common interest. To address these limitations, here we propose a semi-device independent multi-user QPQ scheme exploiting the verification of distributed multipartite GHZ states and the self-testing of a specific class of POVM operators used by the clients. Our scheme allows each user to retrieve different items simultaneously while keeping their choices confidential and also enables the users to retrieve optimal raw key bits during oblivious key generation phase. Additionally, we perform a formal evaluation of the security concerns and are able to determine the maximum likelihood of cheating for both the server and users.