Single-Qubit Loss-Tolerant Quantum Position Verification Protocol Secure against Entangled Attackers

We give a tight characterization of the relation between loss tolerance and error rate of the most popular protocol for quantum position verification, which is based on BB84 states. Combining it with classical information, we show, using semidefinite programming, for the first time a fault-tolerant protocol that is secure against attackers who preshare a linear amount of entanglement (in the classical information), arbitrarily slow quantum information and that tolerates a certain amount of photon loss. We also extend this analysis to the case of more than two bases, showing even stronger loss tolerance for that case. Finally, we show that our techniques can be applied to improve the analysis of one-sided device-independent quantum key distribution protocols.