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

2026-05-28

AI Summary

This work addresses a fundamental limitation in existing quantum position verification schemes, which fail to prevent multiple colluding adversaries from spoofing a location—thereby violating the core semantic guarantees of position-based cryptography. To resolve this, we propose a novel paradigm based on quantum anchor states that uniquely bind unclonable quantum information to a designated spacetime point and enable verifiable tracking of its trajectory. Introducing the notions of quantum anchoring and functional anchoring, we construct a protocol in the classical oracle model and provide a heuristic instantiation leveraging post-quantum indistinguishability obfuscation. In the ideal model, our protocol is provably secure, ensuring that both the quantum state and its associated computational capabilities can be executed exclusively at the specified spacetime location, thereby establishing a rigorous foundation for position-based cryptography.

Abstract

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 localization, which requires that there is a specified, unclonable state at the verified spacetime point -- and that this state can be found nowhere else. We show that quantum localization leads naturally to a meaningful notion of trajectory verification, in which quantum information is verifiably tracked through space and time. We construct quantum localization and trajectory verification protocols using quantum anchor states, which generalize coset states from unclonable cryptography. The security of our schemes is proven in the classical oracle (i.e. ideal obfuscation) model, which can be heuristically instantiated in the plain model using post-quantum indistinguishability obfuscation. We also introduce and instantiate the concept of functionality localization, which guarantees that the adversary has the ability to compute a secret function at the verified spacetime point, and this function cannot be computed anywhere else. This raises the intriguing possibility of localizing computational capabilities in space and time. More broadly, we believe our notions of quantum localization and our feasibility results provide stronger foundations for position-based cryptography.

Problem

• quantum localization
• position verification
• trajectory verification
• unclonable state
• functionality localization

Innovation

• quantum localization
• trajectory verification
• quantum anchor states
• functionality localization
• position-based cryptography