A Quantum Protocol for Millionaire Problem with Continuous Variables

In this paper, a protocol for quantum millionaire problem with continuous variables is proposed. In the protocol, two participants can compare the values of their fortune with the assistance of a semi-trusted third party(STTP). Only EPR states are exploited in our protocol while most other protocols exploited d-dimensional Bell states.Two participants are just required to perform single particle operations, which makes our protocol more efficiently. Our protocol can ensure fairness, correctness, security and high efficiency as well. In our protocol, only the two participants can deduce the results of comparisons, others include STTP will learn no information. Our protocol can resist various kinds of attacks from both the outside eavesdroppers and the inside participants, even the STTP.