Quantum Coin

Quantum Money is a unique object generated by a Trusted Third Party (TTP). Then, it is circulated among untrusted clients (Transferability property). Each client should be able to prove the authenticity of his owned quantum money to a verifier. On the other hand, an adversary must fail in counterfeiting the quantum money with overwhelmingly high probability (Unforgeability property).

Tags: Multiparty, Quantum Enhanced Classical functionality, prepare (bank) and measure (client)

Outline

In this scheme, a Trusted Third Party (TTP) and a coin holder run the following procedure for generating and verifying a quantum coin:

• Quantum coin Generation - The TTP chooses k random 4-bit strings, keeps them in secret and produce k quantum states. A newly issued quantum coin consists of a piece of paper glued to k quantum registers that hold k quantum states. The piece of paper contains a unique identification tag and k initially unmarked positions, where the i-th position has to be marked in k-bit classical register P when the corresponding quantum state is used in the verification protocol.
• Quantum coin Verification - To verify a quantum coin through classical communication with the TTP, its holder sends the identification number of the quantum coin to the TTP. Then, the TTP and the coin holder exchange some classical information for choosing some quantum registers. The coin holder measures the chosen registers and sends their corresponding classical information to the TTP. The TTP verifies the authenticity of the coin by the secret information he possesses.

Properties

• Parameters: HMP₄-states, Let x ∈ {0, 1}⁴. The corresponding HMP₄-states is |α(x)>\myeq\dfrac{1}{2}\sum_{1\leq i\leq4}(-1)^{x_i}\ket{i}

• General Features:

*** No need to quantum communication for quantum coin verification. ** The classical communication channel used for verification can be unencrypted. ** The database of the bank is static, and therefore many de-centralized “verification branches” can exist that do not have to communicate with one another. ** The number of verifications that a quantum coin can go through is limited.

\paragraph{Security Claims} \begin{itemize} \item The coins are exponentially hard to counterfeit. \item secure against an adversary who uses adaptive “attempted verifications” in order to collect information about a coin. \end{itemize}