Noise-tolerant public-key quantum money from a classical oracle

Abstract

Quantum money is the task of verifying the validity of banknotes while ensuring that they cannot be counterfeited. Public-key quantum money allows anyone to perform verification, while the private-key setting restricts the ability to verify to banks, as in Wiesner's original scheme. The current state of technological progress means that errors are impossible to entirely suppress, hence the requirement for noise-tolerant schemes. We show for the first time how to achieve noise-tolerance in the public-key setting. Our techniques follow Aaronson and Christiano's oracle model, where we use the ideas of quantum error correction to extend their scheme: a valid banknote is now a subspace state possibly affected by noise, and verification is performed by using classical oracles to check for membership in "larger spaces." Additionally, a banknote in our scheme is minted by preparing conjugate coding states and applying a unitary that permutes the standard basis vectors.