Quantum Lightning Never Strikes the Same State Twice. Or: Quantum Money from Cryptographic Assumptions

Abstract

Public key quantum money can be seen as a version of the quantum no-cloning theorem that holds even when the quantum states can be verified by the adversary. In this work, we investigate quantum lightning, a formalization of “collision-free quantum money” defined by Lutomirski et al. [ICS’10], where no-cloning holds even when the adversary herself generates the quantum state to be cloned. We then study quantum money and quantum lightning, showing the following results: Thus, we provide the first constructions of public key quantum money from several cryptographic assumptions. Along the way, we develop several new techniques including a new precise variant of the no-cloning theorem.