A verification scheme using quantum states as part of a banknote or token. Secret-basis qubits can make extra copies hard to produce because their encodings are nonorthogonal. Security claims must specify the adversary's information, access to original tokens and the verification procedure; the no-cloning theorem alone does not fix every forging probability.
If a known classical bit is independently encoded in a secret uniformly chosen X or Z eigenbasis, the averaged verification operator is . Its largest eigenvalue is the displayed optimal acceptance probability for a counterfeit prepared without the original qubit. The maximizing state bisects the two candidate Bloch directions. For independent secret bases, the maximal all-pass probability is the th power, because the total acceptance operator is a tensor product. Randomly choosing one of the legitimate encodings instead passes with probability per bit.
