Implementing quantum anonymous multi-party ranking: the influence and application of the law of large numbers

Secure multi-party ranking is not only a pivotal component within the domain of secure multi-party computation but also holds extensive real-world applicability, given its efficacy in safeguarding the integrity and privacy of data. In this paper, we propose a verifiable quantum anonymous multi-party ranking protocol, which leverages the power of multi-particle entangled states in conjunction with the law of large numbers. The protocol achieves the secure ranking of participants' private data while verifying their identities through the assistance of a semi-honest third party. We prove that the protocol is resistant to different types of attacks from internal or external attackers. In addition, the proposed protocol employs qubits as the information carriers, which improves the feasibility of the protocol. We demonstrate the feasibility of the protocol by using the online analog quantum computer of IBM Corporation placed on the cloud. Our research represents an innovative initiative that merges the realms of quantum cryptography and statistical analysis to address pertinent practical challenges.