Breaking the Bounded Entanglement Barrier for Quantum Position Verification
A BB84-based quantum position verification protocol stays secure against LOCC adversaries with arbitrary finite entanglement.
Classical position verification is impossible, and standard quantum position verification fails against LOCC attackers holding exponential preshared entanglement. The authors give a BB84-based protocol that, in an idealized continuous-time model, stays secure against any finite LOCC coalition with arbitrary finite entanglement and storage. A discrete-time version keeps honest communication and storage polynomially below the adversarial resource bound, with the gap growing as clock precision improves.
- Continuous-time BB84 QPV resists finite LOCC adversaries with arbitrary entanglement.
- Discrete-time version yields a polynomial honest-versus-adversary resource gap.
- The resource gap widens as clock timing precision improves.
Full article274 words · extracted from arxiv.org · click to collapse
Position verification, introduced by Chandran et al. (SIAM J. Computing 2014), allows verifiers to test a prover's claimed position by an interactive protocol. Classical position verification is impossible. Even for Quantum Position Verification (QPV), there always exists an LOCC (Local Operations and Classical Communication) attack if the adversary can hold an exponentially large amount of preshared entanglement. Somewhat surprisingly, we show that we can circumvent this barrier in the idealized continuous-time model, where time is represented by a real-valued parameter and challenge messages can be sent at a time sampled uniformly from a real interval. In this model, we give a BB84-based protocol that remains secure against any finite coalition of LOCC adversaries with arbitrary finite (possibly exponential) quantum storage and entanglement. Our construction can also be instantiated in the discrete-time model. Even though the previous impossibility results apply, we are able to obtain an information-theoretic QPV protocol in which the honest parties' total resources (communication and storage) can be significantly smaller than the adversarial resource bound. In fact, we can achieve any desired polynomial gap between honest parties and adversarial resources. To our knowledge, all previous protocols in the literature required resources of the honest parties to be at least as large as the adversarial entanglement. Interestingly, the resource gap between the honest and adversarial party resources in our protocol depends on how precisely time can be measured. As the precision of the best-known clock improves with further research, the resource gap in our protocol keeps increasing. In particular, the adversarial resource bound keeps increasing while the honest parties' resources remain largely the same. We call this the "I sleep, you work" paradigm.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.39234