A General Quantum Duality for Representations of Groups - Applications to Quantum Money, Lightning, and Fire

Watch a 79-minute lecture from QuICS exploring a groundbreaking quantum duality principle for group representations and its applications to quantum cryptography. Delve into how swapping quantum states is computationally equivalent to distinguishing their superpositions, extending this to a broader principle where manipulating states in one basis equals extracting values in a complementary basis. Learn about novel applications including the first secure quantum lightning construction in the plain model based on non-Abelian group actions, an alternative construction from one-way homomorphisms showing equivalence between different security notions, and a new candidate for quantum fire states using classical oracles rather than requiring unitary oracles. Understand how these advances impact quantum money, quantum lightning, and quantum fire implementations while exploring the mathematical foundations connecting group theory, quantum mechanics, and cryptography.