Before revision:  Rev. A 84, 010302 (2011) with more restrictive condition for acceptance. This is in correspondence with more complex proof of security originating from a two-party cryptographic nature of the money schemes. The lower bound on the size of the banknote is ruled only by the law of large numbers as the secure key is not physically generated during the protocol. Due to the current burst out of the new quantum-crypto currencies, on the basis of the presented protocol we finally introduce and discuss possible quantum analogue of the Oresme-Copernicus-Gresham's law of economy.
After revision:  Rev. A 84, 010302 (2011) quantum key distribution protocol, we introduce the first scheme of quantum money with this assumption partially relaxed, along with the proof of its URLeability. Significance of this protocol is supported by an impossibility result, which we prove, stating that there is no both fully device independent and secure money scheme. Finally, we formulate a quantum analogue of the Oresme-Copernicus-Gresham's law of economy.