How To Track Qubits Through Space and Time (Or: Sailing in a Quantum Boat)

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While quantum position verification aims to certify a prover's location using quantum information, existing security definitions only guarantee that part of the successful adversarial party is in the claimed location. This leaves open the possibility that a distributed team of adversaries can jointly simulate a prover in a way that defeats the intended meaning of ``being at a location'' in position-based cryptography. We introduce stronger notions of position verification that we call quantum