Quantum Money and Wiesner's Protocol

Quantum Money and Wiesner's Protocol

Quantum money, proposed by Stephen Wiesner around 1970 (and published in 1983), is one of the earliest applications of quantum mechanics to cryptography: predating BB84 by more than a decade. It exploits the no-cloning theorem to create unforgeable banknotes.

The Basic Concept

The bank keeps a secret record: for each serial number, which state was encoded in each qubit. States are chosen from the four BB84 basis states: |0⟩, |1⟩, |+⟩, |−⟩.

Verification: The note holder presents the note to the bank. The bank looks up the serial number, measures each qubit in the correct basis, and checks that the result matches the secret record. A legitimate note passes with probability 1. A counterfeiter who does not know the secret record must guess the basis for each qubit. With n qubits, the probability that all measurements pass is $(3/4{)}^n$: exponentially small.

The No-Cloning Guarantee

Why can't a counterfeiter copy the quantum states? The no-cloning theorem: an unknown quantum state cannot be perfectly copied. If the qubit is in state |+⟩ (which is a superposition of |0⟩ and |1⟩), any measurement reveals only a single bit of information, collapsing the state. The other 3 possible states are compatible with the same measurement outcome, so the counterfeiter cannot determine which state was prepared.

For $n=20$ qubits, the counterfeiting probability is $(3/4{)}^{20}\approx 0.003$ (0.3%). For $n=100$ qubits: $(3/4{)}^{100}\approx 3\times 10^{-13}$. This is the quantum money security guarantee.

Practical Limitations

Quantum money faces a storage problem: quantum states decohere quickly (current quantum memories last milliseconds to seconds). Keeping the qubits coherent in a banknote for weeks while it circulates in the economy is beyond current technology.