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

TL;DR

This paper introduces simple quantum protocols for the millionaire problem with a third party, requiring only quantum key distribution and offering improved security with minimal information leakage.

Contribution

It presents novel, straightforward quantum protocols that leverage quantum key distribution, surpassing previous complex methods in security and simplicity.

Findings

Protocols require only quantum key distribution.

Information leakage can be minimized arbitrarily.

Dishonest third parties cannot compromise the protocols.

Abstract

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