Quantum Private Magnitude Comparison

As we all know, the comparison of two numbers will bring about one of the three results: greater than, equal and less than. Quantum private comparison (QPC) uses the properties of quantum mechanics to provide security for private comparison. However, its many existed researches could only output one of the two outcomes: equality and inequality, generally. The paper calls this kind of QPC as quantum private identity comparison (QPIC), and names QPC with the three results above as quantum private magnitude comparison (QPMC). Nowadays, it is seldom mentioned and studied. In order to make QPC function as not only QPIC, but also QPMC, the paper proposes a QPMC protocol, which can resolve the issues like the well-known millionaire problem, telling two millionaires whose wealth is more without leaking their actual values. To this end, the article introduces a basic operation at first, and then employs Bell states as quantum resources to implement the QPMC protocol. At last, it is analysed fully to show its correctness and security. The presented protocol is simple yet effective, easy to implement with common technologies.