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Recently there were many quantum protocols devoted to solve the millionaireproblem and private comparison problem by adding a semi-honest third party.They all require complicated quantum methods, while still leak a non-trivialamount of information to at least one of the parties. But it will be shown herethat once the third party is introduced, there are very simple protocols whichrequire quantum key distribution as the only quantum resource, and the amountof information leaked can be made arbitrarily small. Furthermore, even adishonest third party cannot spoil the protocols. Thus our solutions surpassall existing protocols on both feasibility and security.

Quantum protocols for the millionaire problem with a third party are trivial