When communication is expensive, the important task of testing two binary strings for equality can be achieved by generating relatively short fingerprints of each string and comparing those fingerprints. Quantum fingerprinting, in which the fingerprint is encoded onto qubits (the quantum version of the bit), is significantly less expensive: exponentially better in the case of no shared randomness and potentially perfect for the case of shared entanglement. Single-qubit quantum fingerprinting is feasible, and we have demonstrated its advantages theoretically and experimentally.