A Multiparty Quantum Private Equality Comparison scheme relying on ket{ GHZ ₃ } states

This paper introduces an innovative entanglement-based protocol that accomplishes multiparty quantum private comparison leveraging maximally entangled GHZ3 triplets. The primary motivation is the design of a protocol that can be executed by contemporary quantum computers. This is made possible because the protocol uses only GHZ3 triplets, irrespective of the number of millionaires. While more complex multi-particle entangled states are possible, they are challenging to produce with existing quantum apparatus, leading to extended preparation time and complexity, particularly in scenarios involving numerous participants. By relying on GHZ3 states, which are the easiest to produce after Bell states, we avoid these drawbacks, and take a step towards the practical implementation of the protocol. An important quantitative characteristic of this protocol is that the required quantum resources are linear both in the number of millionaires and the volume of information to be compared. A notable aspect of the protocol is its suitability for both parallel and sequential execution. Although the execution of the quantum part of the protocol is envisioned to take place completely in parallel, it is also possible to be implemented sequentially. So, if the quantum resources do not suffice for the execution of the protocol in one go, it is possible to partition the millionaires into smaller groups and process these groups sequentially. Notably, our protocol involves two third parties; Trent is now accompanied by Sophia. This dual setup allows simultaneous processing of all n millionaires' fortunes. Implementation-wise, uniformity is ensured as all millionaires use similar private quantum circuits composed of Hadamard and CNOT gates. Lastly, the protocol is information-theoretically secure, preventing outside parties from learning about fortunes or inside players from knowing each other's secret numbers.