Breaking the Bounded Entanglement Barrier for Quantum Position Verification

2026-09-30

AI Summary

This study addresses the bottleneck in quantum position verification (QPV) where adversaries exploit large amounts of pre-shared entanglement to launch attacks. We propose novel BB84 protocols under both continuous- and discrete-time models. The continuous-time model is proven secure against arbitrary finite LOCC attacks, while the discrete-time model introduces a pioneering "I-sleep-you-work" paradigm that maintains constant resource overhead for honest parties, whereas the resources required by adversaries grow exponentially with increasing measurement precision. This work achieves information-theoretically secure QPV with an arbitrary polynomial gap between honest and adversarial resource requirements, thereby overcoming the security limitations inherent in all prior protocols.

Abstract

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.

Problem

• Quantum Position Verification
• Bounded Entanglement
• LOCC attack
• Resource gap
• Preshared entanglement

Innovation

• Quantum Position Verification
• Bounded Entanglement
• Continuous-time Model
• Resource Gap
• BB84 Protocol