Llorenç Escolà-Farràs

Signal loss poses a significant threat to the security of quantum cryptography when the chosen protocol lacks loss-tolerance. In quantum position verification (QPV) protocols, even relatively small loss rates can compromise security. The goal is thus to find protocols that remain secure under practically achievable loss rates. In this work, we modify the usual structure of QPV protocols and prove that this modification makes the potentially high transmission loss between the verifiers and the prover security-irrelevant for a class of protocols that includes a practically-interesting candidate protocol inspired by the BB84 protocol. This modification, which involves photon presence detection, a small time delay at the prover, and a commitment to play before proceeding, reduces the overall loss rate to just the prover’s laboratory. The adapted protocol then becomes a practically feasible QPV protocol with strong security guarantees, even against attackers using adaptive strategies. As the loss rate between the verifiers and prover is mainly dictated by the distance between them, secure QPV over longer distances becomes possible. We also show possible implementations of the required photon presence detection, making the adapted protocol a protocol that solves all major practical issues in QPV. Finally, we discuss experimental aspects and give parameter estimations.

Motivated by the fact that coherent states may offer practical advantages it was recently shown that a continuous-variable (CV) quantum position verification (QPV) protocol using coherent states could be securely implemented if and only if attackers do not pre-share any entanglement. In the discrete-variable (DV) analogue of that protocol it was shown that modifying how the classical input information is sent from the verifiers to the prover leads to a favourable scaling in the resource requirements for a quantum attack. In this work, we show that similar conclusions can be drawn for CV-QPV. By adding extra classical information of size $n$ to a CV-QPV protocol, we show that the protocol, which uses a coherent state and classical information, remains secure, even if the quantum information travels arbitrarily slow, against attackers who pre-share CV (entangled) states with a linear (in $n$) cutoff at the photon number. We show that the protocol remains secure for certain attenuation and excess noise.

Extended non-local games are a generalization of monogamy-of-entanglement games, played by two quantum parties and a quantum referee that performs a measurement on their local quantum system. Along the lines of the NPA hierarchy, the optimal winning probability of those games can be upper bounded by a hierarchy of semidefinite programs (SDPs) converging to the optimal value. Here, we show that if one extends such games by considering constraints and loss, motivated by experimental errors and loss through quantum communication, the convergence of the SDPs to the optimal value still holds. We give applications of this result, and we compute SDPs that show tighter security for certain protocols in quantum cryptography such as relativistic bit commitment, quantum key distribution and quantum position verification.