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Public-key quantum money is a cryptographic proposal for using highlyentangled quantum states as currency that is publicly verifiable yet resistantto counterfeiting due to the laws of physics. Despite significant interest,constructing provably-secure public-key quantum money schemes based on standardcryptographic assumptions has remained an elusive goal. Even proposingplausibly-secure candidate schemes has been a challenge.  These difficulties call for a deeper and systematic study of the structure ofpublic-key quantum money schemes and the assumptions they can be based on.Motivated by this, we present the first black-box separation of quantum moneyand cryptographic primitives. Specifically, we show that collision-resistanthash functions cannot be used as a black-box to construct public-key quantummoney schemes where the banknote verification makes classical queries to thehash function. Our result involves a novel combination of state synthesistechniques from quantum complexity theory and simulation techniques, includingZhandry's compressed oracle technique.

On the (Im)plausibility of Public-Key Quantum Money from Collision-Resistant Hash Functions