Quantum sealed-bid auction using the phases of quantum entangled states as bids

Today, various processes are being carried out on the Internet. Therefore, we need to think about security on the Internet since various confidential information is also communicated. Quantum information such as quantum cryptography also plays an important role in the security. Moreover, many quantum applications are also proposed. In this paper, we focus on sealed-bid auction on the Internet and propose a quantum sealed-bid auction with entanglement. The advantage of our protocol is that it uses the phases of quantum entangled states as bid prices. Therefore, no one, including legitimate parties, can steal useful information such as bid prices unless all the states are obtained. As a result, any information is not leaked to any outside attacker, bidders cannot know each other's bid prices, and the auctioneer can only obtain the highest bid price.