Quantum Money Generated by Multiple Untrustworthy Banks

While classical money can be copied, it is impossible to copy quantum money in principle, with only the bank that issues it knowing how to generate it, meaning only the bank can make exact copies. Not all reliable banks, such as central banks, will issue quantum money, so there is the possibility that untrustworthy banks are distributing fake or multiple copies of the same quantum money without the users' knowledge. As such, we propose a quantum patchwork money scheme in which banks cannot distribute exact copies to users. This scheme involves multiple banks providing public-key quantum money as shards and generating quantum patchwork money by combining them. The banks can use the quantum patchwork money without completely trusting the other banks. In addition, nonbank users can use safely the quantum patchwork money without trusting any banks potentially focused on self-interest by adding a protocol for monitoring the distribution of copies.Comment: 21 page