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Public key quantum  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, investigate quantum lightning, a formalization of collision-free quantum money defined by Lutomirski et al. [ICSu002710], where no-cloning holds even when the adversary herself generates the quantum state to be cloned. We then study quantum  and quantum lightning, showing the following results: - We demonstrate the usefulness of quantum lightning by showing several potential applications, such as generating random strings with a proof of entropy, to completely decentralized cryptocurrency without a block-chain, where transactions is instant and local. - We give win-win results for quantum money/lightning, showing that either signatures/hash functions/commitment schemes meet very strong recently proposed notions of security, or they yield quantum  or lightning. - We construct quantum lightning under the assumed multi-collision resistance of random degree-2 systems of polynomials. - We show that instantiating the quantum  scheme of Aaronson and Christiano [STOCu002712] with indistinguishability obfuscation that is secure against quantum computers yields a secure quantum  scheme

Quantum Lightning Never Strikes the Same State Twice