Quantum fingerprinting

Quantum fingerprinting is a proposed technique that uses a quantum computer to generate a string with a similar function to the cryptographic hash function. Alice and Bob hold ${\displaystyle n}$-bit strings ${\displaystyle x}$ and ${\displaystyle y}$. Their goal and a referee's is to obtain the correct value of ${\displaystyle f(x,y)={\begin{cases}1&{\text{if }}x=y,\\0&{\text{if }}x\neq y.\\\end{cases}}}$. To do this, ${\displaystyle 2^{n}}$ quantum states are produced from the O(logn)-qubit state fingerprints and sent to the referee who performs the Swap test to detect if the fingerprints are similar or different with a high probability.^[1]

If unconditional guarantees of security are needed, and if it is impractical for the communicating parties to arrange to share a secret that can be used in a Carter–Wegman MAC, this technique might one day be faster than classical techniques given a quantum computer with 5 to 10 qubits. However, these circumstances are very unusual and it is unlikely the technique will ever have a practical application; it is largely of theoretical interest.