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Quantum Amnesia Leaves Cryptographic Mementos: A Note On Quantum Skepticism

Leonard Shelby, the protagonist of Memento, uses mementos in the form of tattoos and pictures to handle his amnesia. Similar to Leonard, contemporary quantum computers suffer from "quantum amnesia": the inability to store quantum registers for a long duration. Quantum computers can only retain classical "mementos" of quantum registers by measuring them before those vanish. Some quantum skeptics argue that this quantum amnesia is inherent. We point out that this variant of a skeptic world is roughly described by the quantum bounded storage model, and although it is a computational obstacle that annuls potential quantum computational advantage, the seemingly undesired properties provide a cryptographic advantage. Namely, providing exotic primitives promised by the quantum bounded storage model, such as unconditionally secure commitment and oblivious transfer schemes, with constructions involving nothing but transmission and measurement of BB84 states.