Quantum Money

Quantum Money is a quantum cryptographic scheme that was first introduced by Wiesner [Wie83] in 1983. Informally, a quantum coin is a unique object that is created by a Trusted Third Party (TTP). Then, it is circulated among untrusted clients (Transferability property). Each client should be able to verify it and confirm that it is authentic if it has been circulated according to the prescribed rules. On the other hand, an adversary must fail in counterfeiting it with overwhelmingly high probability (Unforgeability property). The quantum money schemes can be classified in two categories: Public Quantum Money and Private Quantum Money.

Outline

Assume a TTP (eg. a bank), a verifier (eg. a merchant) and a prover (eg. a client) are involved in a quantum money scheme. Also, assume there is only one circulating quantum coin. They follow the following procedure: \begin{itemize} \item[] \textbf{Preparation} TTP prepares $n$ qubits for each quantum coin with a serial number S. It stores the classical information about the qbits corresponding to S in a database and handover the quantum coin to a prover. \item[] \textbf{Interaction} In this step, the prover wants to transfer the quantum coin to a verifier. So, the authenticity of the quantum coin shall be verified by the verifier. To this end, the verifier sends a challenge to the prover and gets the serial number $SN$ of the quantum coin and the prepared qbits for it. \item[]\textbf{Transaction} The verifier accepts the coin if the received qbits corresponds to the stored information in the database regarding the serial number and classical information of the quantum coin. If the verifier can do the verification process by his own, the quantum money scheme is called public quantum money. Otherwise, if he needs to communicate with the TTP to verify the quantum coin, the scheme is called private quantum money. \end{itemize}